I read several places that the obsidian lite sound card is not 'supposed' to work well with rechargeable lithium batteries, but after finding the specs on the board and attempting to upgrade my own obsidian-lite powered saber I can attest that this was pure myth and mine now runs just GREAT on a single 18650 li-ion cell! Here's a link to the specs:
http://rsxengineering.com/saber_resources/ObsidianLite_Datasheet.pdfWhich clearly indicate the board can run on anywhere between 3.5 and 5.5V DC input. The 'normal' setup with 4xAAA batteries is right in the middle at about 4.5V (NiMH) or 5.5V (Alkaline), but of course both of these lose a good bit of voltage as they drain and drop to more like 4.0V or less once they're about 2/3 discharged. A 3.7V lithium cell is also right about 4.0V fully charged, but the li-ion batteries hold up their voltage MUCH better even when 90% discharged, so this is still within the operating voltage range of the card.
So I got to hacking, popped out the speaker, unscrewed the speaker holder from the battery pack, cut out the old AAA battery pack, soldered in the new 18650 holder, screwed the speaker holder onto the new holder, and put it all back together, and so far it's working like a CHAMP! By the numbers, the single 18650 should have about 3x as much capacity (~12Wh) as 4xAAAs (~4Wh), so that's pretty substantial. Link to pic below!
Of final note, you should NOT use 2x Li-ion cells in series with an Obsidian-Lite card (like the 2x 14500 cells offered with Obsidian-USB boards) as that voltage will be too high for the Lite. You SHOULD however to be able to use either a single OR 2x series 18650 cells to run an Obsidian-USB card, as it's stated voltage range is 3.5-9V DC, although since I don't have one of these boards, I haven't actually tested that myself.
Pic for proof:
https://photos.app.goo.gl/JN3KCTYNM6KMFnJV9