1491 DR
Ed Greenwood gave an answer to this on Twitter:
Lost Mine is officially a bit nebulous in date for DM convenience, though there are detailed internal WotC timelines so as to keep things straight (i.e. novels). Safe to say: 1490s DR.
Of course, his tweets aren't official source material, but they give a small glimpse behind the curtain at designer intent, and are a reminder that all these dates have an important context: the metaplot.
The Forgotten Realms metaplot
The Forgotten Realms setting has a metaplot that continues to advance chronologically with new source material, and new editions of the game. For example, when the 4th edition of D&D came out, the metaplot advanced by about a century.
The first 4th Edition campaign setting releases later this summer, with a new look at the Forgotten Realms. If you've read the previews, you'll know by now that major changes have affected the Realms: starting with the Spellplague and the 100-year advancement of the timeline.
4e material
The century of advancement in the setting resulted in a lot of drastic changes to the world. The 4e Forgotten Realms Campaign Guide (2008) notes:
Ten Important Facts
The following points describe the biggest changes
to the world of Toril since the previous edition of
the FORGOTTEN REALMS Campaign Setting. If you are
familiar with the setting, these will summarize the
major events in the world since 1374 DR, the Year of
Lightning Storms. If you are new to the setting, this
information will give you the basic background that
most inhabitants know.
- Roughly a hundred years have passed in the world
since the previous edition of the campaign setting. The
current year is 1479 DR, the Year of the Ageless One.
- The Spellplague has drastically altered the cosmos.
The Spellplague broke out in 1385 DR (the Year of
Blue Fire), the result of unfettered wild magic on the
death of the goddess Mystra. Whole countries are
gone, especially in regions south of the Sea of Fallen
Stars. [...]
And so on. Flying islands in the sky called "earthmotes." A continent that wasn't there before on the other side of the Trackless Sea. Like New Coke, all these 4e changes were rapidly done away with in the transition to 5e, as a result of a cross-media event called "The Sundering" announced in 2012.
In 2013, the D&D Encounters adventures began to take part in The Sundering plotline starting with D&D Encounters season 15: Murder in Baldur's Gate. Being in a transitional period, the module was written to be playable with any of three editions of D&D: 3.5e, 4e, or 5e (then called "D&D Next").
5e material
"A Brief History" in Sword Coast Adventurer's Guide directly alludes to the events in Murder in Baldur's Gate and The Sundering plotline (calling it "The Second Sundering" since there was also an earlier cataclysm by that name):
The first indication of new turmoil came in 1482 DR, when Bhaal, the long-dead god of murder, was reborn in Baldur’s Gate amid chaos and bloodshed, leaving two of the city’s dukes and many of its citizens dead.
And it caps off the history of the Realms with establishing a present day status quo that has hit the reset button on most of those setting alterations from 4e, with everything noticeably "much like it was" before "that terrible time." The present day being 1489 DR or later:
Early in 1487, earthquakes and volcanic eruptions abounded for months, as if the whole world was convulsing. Rumors spread of chasms caused by the Spellplague suddenly vanishing, and stories circulated of known destinations being farther away from one another, as if the world had quietly added miles of wilderness to the distance between them. Word began to spread of places and peoples not heard from since the Spellplague. It became apparent that some of the effects of that terrible time had been reversed.
By 1489, many of the wars that began during the Sundering had ground to a close. Other conflicts arose, and mighty threats still imperiled the world, but the deities ceased interfering with the world through their Chosen. The gods were no longer silent but quiet, and in many places new priesthoods arose to interpret the gods’ now subtle signs.
The world today seems a place filled with new lands and opportunities, where those who dare can leave their mark. Students of history and those elves and dwarves who recall the past that short-lived humans see as distant perceive a world much like it was over a century ago.
So this is the context in which Ed Greenwood said that LMoP definitely occurs in the 1490s: that's roughly where the metaplot left off when 5e began.
So when is Lost Mine of Phandelver?
Official material wise, Acquisitions Incorporated contains an adventure explicitly set five years after Lost Mine of Phandelver:
HAVE WE BEEN HERE BEFORE?
The town of Phandalin will be recognizable to any players familiar with the Lost Mine of Phandelver adventure. This version of Phandalin is set five years or so after that adventure, making use of many of the original Phandalin locations and NPCs even as it adds new places and new characters to the mix. If you have your own version of Phandalin in your campaign, make any adjustments necessary to this episode for continuity.
The same adventure is also set five years after Princes of the Apocalypse:
The Princes of the Apocalypse adventure contains more information on Red Larch and the surrounding region. As with Phandalin, this version of Red Larch is set about five years later than that earlier adventure.
And Princes of the Apocalypse is explicitly set in 1491 DR:
TIME IN THE REALMS
The people of the Forgotten Realms number the years by the Dalereckoning calendar, which is abbreviated “DR.” Years are also given names, which are drawn from the writings of a great seer from long ago. The adventure is set in 1491 DR, the Year of the Scarlet Witch.
Each month consists of three ten-day long weeks called tendays. People refer to tendays the way people in other worlds refer to weeks.
Since Acquisitions Inc establishes that LMoP and PotA are set around the same time, LMoP occurs in 1491 DR.
Given that as a general rule, newly published material seems to be set in the 'present day' of the ever-advancing Forgotten Realms metaplot, 1491 DR is a lot more credible than the seemingly contradictory line in LMoP that claims the famous eruption of Mount Hotenow in the early 1450s occurred only 30 years prior.
But when did Mount Hotenow erupt?
The eruption of Mount Hotenow, a historical event that only exists in novels set in the long timeskip between 3e and 4e, has been fuzzy for a while now. The 4e book Neverwinter Campaign Setting (2011) repeatedly implies it happened in 1452 DR (it says 'twenty-seven years ago' four different times), but one sentence instead implies it was 1453 DR.
The current year is 1479 DR.
When the primordial Maegera erupted from its prison
twenty-six years ago, the resulting volcanic destruction
tore a deep chasm in the earth that sliced through a
quarter of Neverwinter.
At that time, twenty-seven years ago, Maegera
stirred in its slumber, and its dream of ruination
was enough to destroy the city.
In 5e, Sword Coast Adventurer's Guide shrugs and keeps it vague and nebulous precisely what year it happened:
Nearly half a century ago, Mount Hotenow (the nearby volcano that perpetually heats the river flowing through the city) violently erupted, destroying much of Neverwinter, killing thousands, and leaving in its wake a great, gaping chasm that split the city. Neverwinter was in ruins, and external influences—from Netheril to Thay to Lord Dagult Neverember of Waterdeep to the agents of the Hells themselves—sought to exert control over the city. Many folk fought to stem all these dangers, and eventually, a measure of peace fell over Neverwinter.
But then, in multiple other books, this vague and nebulous phrase 'nearly half a century' (that could plausibly describe a span of time anywhere from 40 to 49 years, and seems likely to be 40 years in this case) gets replaced with much more precise but inaccurate numbers.
LMoP interprets it as 'thirty years,' so that it's within living memory of a certain commoner NPC.
Quest: Mirna's Heirloom. Though her family has nothing to offer as a reward, Mirna tells the characters that she might know where a valuable heirloom is hidden. When she was a young girl, she and her family fled from the town of Thundertree after undead overran the place.
Near the place where the Neverwinter River emerges from Neverwinter Wood stands the abandoned village of Thundertree. Once, this was a prosperous community on the outskirts of the forest, wealthy from the work of its woodcutters and trappers. Then thirty years ago, the eruption of Mount Hotenow to the north devastated Thundertree. In the wake of the natural disaster, a plague of strange zombies swept over the area, killing or driving off those who survived the eruption.
Princes of the Apocalypse says it's 'about' fifty years ago.
The city of Neverwinter lies on the Sword Coast, west and north from the Dessarin Valley. Once known as the Jewel of the North, Neverwinter was badly damaged when nearby Mount Hotenow erupted about fifty years ago. The City of Skilled Hands works furiously to rebuild itself as a wealthy trading city known for its clocks and other superbly made local items. Neverwinter's reconstruction is far from complete, however. Entire sections of the city still lie in rubble, plagued by brigands and monsters, and sinister factions scheme to take over the place.
Hoard of the Dragon Queen is a real outlier:
By asking around, characters learn that the road to the north, called the High Road, used to connect Waterdeep to the city of Neverwinter. A cold, coastal marsh called the Mere of Dead Men lay between the road and the coast. Over the years, the mere continually expanded. Each time it grew, it flooded the road, which had to be relocated farther inland. That was the situation until a century ago, when Neverwinter was nearly destroyed by the eruption of Mount Hotenow. With the city in ruins, efforts to keep the road open simply stopped. It no longer served a purpose.
Storm King's Thunder:
Once known as the Jewel of the North, the city of Neverwinter was badly damaged when nearby Mount Hotenow (see the "Neverwinter Wood" section) erupted about fifty years ago. Now, the City of Skilled Hands works furiously to rebuild itself. Neverwinter's reconstruction is far from complete, however. Some of its outer walls still lie in ruins, and several of its neighborhoods remain abandoned. Even so, the great chasm to the Underdark that opened within the city has been magically sealed (at great expense), and that achievement bodes well for Neverwinter's future.
Dragon of Icespire Peak (with its 3 sequel adventures, Storm Lord's Wrath, Sleeping Dragon's Wake, and Divine Contention):
Neverwinter
This city was badly damaged when Mount Hotenow erupted some fifty years ago. Now, the City of Skilled Hands works to rebuild under the watchful eye of its Lord Protector, Dagult Neverember, who rules in the absence of an heir to Neverwinter's crown. At present, no legitimate heirs to the old Alagondar royal line are known to exist, and many believe that the line is ended. Lord Neverember, taking no chances, quietly pays off or disposes of anyone claiming a connection to the rulers of old.
