I've researched this further.
LG makes it clear that the only way to get updates is to sign on with a major carrier and get it from them.
For my phone, the current software version is US99122a, but I probably need US99120c, which is for phones not already updated to Marshmallow. Those updates are available from US Cellular, though I see no way to get it from their site without signing up with them--however, my phone is GSM, whereas they're CDMA; will that cause problems? Or am I misunderstanding?
AT&T, which is GSM, has updates, but their G4 version is the 810, so their update is H81022b, and they say "n order to receive the latest software update, you must be on current software version H81021z. If not, repeat the update process until you’ve installed H81021z, and then you should be able to install the most recent software update"
Anyone have any suggestions? I hear that if I root my phone, I can install updates myself--but where would I get the updates in the first place?