There's no current method off purchasing more lanterns.
You /could/ try stringing up the crystals (fear, light/protect, unknown orange, unknown blue)....
But I don't know how well the cave would treat them.. I have ore remain in the cave, but I'm fairly certain I've seen someone mention or maybe I had it happen to me, leaving their lantern and it no longer being there on return/reload
If you try REEEEAAALLLYY hard.... You can lock a crate, inside a crate. - That'll give you maybe 1.5 to 2 crates worth of space (1 crate on top will be full, if you have 3, the other two can't be entirely full, need to have enough room to drop the corner in and QUICKLY lid without it popping back up from physics tension (i.e, full crate)
One crate will likely have lantern in it, and/or a crystal for lighting, keeping such will allow you to hold the crate near the surfaces and see where you're going.
Turning up gamma will help drown blackness out.
Turning down shadows/effects/post processing will drown vignette and a decent bit of darkening effects. - Low is "0" in most cases, which really means "off" - In other cases it means low, namely, view distance.
On cave treatment again - It's possible nothing might happen - its also possible they might somehow get sucked into the void/space behind surfaces during some part of map reload/transition - sometimes it seems to be the only explanation - strange and lacking game-logic as it may seem