You can use the Quickened Spell Metamagic on a spell cast from/using a wand, and it works like any other Metamagic
Stuff about wands
First off, if you cast a spell from a wand you are still casting that spell. This is established in the following two Q/A's:
In particular, the wand of lightning bolts states:
While holding it, you can use an action to expend 1 or more of its charges to cast the lightning bolt spell (save DC 15) from it. For 1 charge, you cast the 3rd-level version of the spell.
Additionally the Activating a Magic Item section of the DMG states, under the "Spells" subsection (page 141):
Some magic items allow the user to cast a spell from the item.
These show that when using a wand, or any magic item you are still the one casting the spell.
We also know that activating/using a wand does not involve the Cast a Spell action nor the Use an Object action. Instead it uses an entirely different action, something like the "Use a Wand" action. We know this from the Activating an Item section of the DMG (page 141):
If an item requires an action to activate, that action isn't a feature of the Use an Item action [...]
Stuff about the Quickened Spell Metamagic
The description of the Quickened Spell Metamagic option
When you cast a spell that has a casting time of 1 action
We are casting the spell, and lightning bolt does have a casting time of 1 action, so that's good.
you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.
Unfortunately, casting time is barely defined by the rules in any real way. What we do know is from the Casting Time section:
Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast [...]
And from the Activating an Item section of the DMG, under the "Spells" subsection (page 141):
[...] The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration [...]
Thus we know that when casting lightning bolt from a wand of lightning bolts it will still have a casting time of 1 action, and, since we are casting the spell (as established earlier), we can apply Quickened Spell to that casting, changing lightning bolt's casting time to a bonus action.
But does this do anything useful?
Using a wand does not involve taking the Cast a Spell action, but Metamagic doesn't require the Cast a Spell action in the first place, so that's good. We are taking the "Use a Wand" action to ultimately cast a spell that has a casting time of 1 action, and have changed the casting time of that spell to 1 bonus action.
Does the action required to use a wand of lightning bolts represent the casting time of the spell? It is literally the amount of time it takes to cast the spell, but how exactly are these two things related (the casting time of a spell and the amount of time it takes to use an item that lets you cast that spell)?
The rod of resurrection points the way
The "Spells" section on Activating an Item also says this:
[...] Certain items make exceptions to these rules, changing the casting time, duration, or other parts of a spell [...]
One example of such an item is the rod of resurrection which states:
The rod has 5 charges. While you hold it, you can use an action to cast one of the following spells from it: heal (expends 1 charge) or resurrection (expends 5 charges).
The resurrection spell ordinarily takes an hour to cast, but this magic item changes its casting time to 1 action.
Using this we can conclude that the casting time of lightning bolt is the same as the amount of time it takes to use the wand of lightning bolts and thus Quickened Spell allows us to use our bonus action to cast lightning bolt.
What is the alternative?
We've already established that you can definitely use Quickened Spell on a spell cast from a Wand. It was just unclear what it actually did.
And so there is an alternative answer: When using a rod of resurrection you are using an action to cast a spell that has a casting time of 1 hour and when using a wand of lightning bolts you are using an action to cast a spell that has a casting time of 1 bonus action (this would mean you've used up your action and you can't cast a spell of 1st level or higher on your current turn). This is a perfectly valid interpretation; it prevents Quickened Spell from working in any meaningful way, but it also results in particularly unusual situations.
Non-rules supporting evidence
It's already established in the following two questions that you can use Metamagic on spells cast from magic items, including spell scrolls specifically:
Given that you can use every single other Metamagic with these spells, why prevent people from using Quickened Spell on them? To me, it would be especially odd that every Metamagic can be used except Quickened Spell.