The Warlock casts spells at one given level.
Spell Slots (PHB, p.107)
... all of your spell slots are the same level. {snip} ... when you are 5th level, you have two 3rd‑level spell slots. To cast the 1st‑level spell Thunderwave, you must spend one of those slots, and you cast it as a 3rd‐‑level spell.
A 4th level Warlock (all spells at second level) can't (at first blush) fill the Ring of Spell Storing because it holds five spell levels but she must cast spells at second level.
Two ways to try and get around this:
Cast two Hold Person spells into the ring (four levels of spell), a short rest, and cast one Faerie Fire (a first level spell). Faerie Fire is now cast at second level since the Warlock only has second level spell slots. Faerie Fire doesn't have an "at higher level" clause; it only acts as a first level spell, so maybe she can in -- but I don't think so. The 'must' in the Warlock spell casting rule looks like a deal breaker.
Her Pact of the Chain Pact Boon allows her to cast a first level spell as a ritual: Find Familiar. (Covered in a separate question). Does that cast as a second level spell as well, or, is that a first level spell, and a special case due to being Pact Boon? If the latter, she could pop that into the ring to fill up the fifth spell level slot (in case the familiar dies). If the former, she could not. The "must" looks like a deal breaker here, even though the pact boon does not burn a slot. Our Warlock may be out of luck, unless ritual overrides the table.
At fifth level, the Warlock could cast Blink (a third level spell), but could not cast the Hold Person spell into the ring since it is now being cast at third level, rather than second level as previously done, and the ring won't hold six spell levels.
Problem to Solve: How can a Warlock of third level or greater1 fill up the Ring of Spell Storing? This is of particular concern when the Warlock is the only spell caster in the party. The only way I see around this is to have another party member cast a lower level spell or two into the ring to fill up the other spell level slots.
Is there another way to do this, or is the Warlock unable to fill a Ring of Spell Storing until she can cast fifth level spells?
1 At first or second level, a Warlock could fill one with five 5 first level spells but a ring dropping that early in the game is unlikely.