We have had the BUMP bootloader unlock method along with custom recovery for the Verizon variant of the LG G3 for several weeks now. So far the only roms to come out have been a stock based Jasmine Rom and a plain stock rooted Rom. Developer "Invisiblek" posted a screenshot of his LG G3 running Cyanogen Mod. He also stated that while it is booting he still has a bit of work to do to make this Rom releasable. He is working on fixing the camera, GPS, and IR. it seems as if he is shooting to release a daily driver rather than just going ahead and releasing a rom full of bugs. I feel it is worth the wait. Once CM is released there should be a good base for any other developers that would like to build an AOSP rom.
Developer "Bunchies" also posted an image of the Liquid Smooth rom running on an LG G3! We should be seeing some AOSP roms releasing very soon.
via XDA