According to a direct response from LG PR rep Ken Hong, LG has no current plans to bring out a Google Edition unlocked version of the LG G2. Here's a quote from him,

”As of right now, LG doesn’t have any plans for a Google Play Edition. The focus for the G2 is penetration through carriers. That however could change down the road.”
Luckily, it looks like he was diplomatic enough to leave wiggle room for a possible future reversal on this. It's probably not too surprising that LG doesn't plan to have a Google Play Edition of the phone. Several of the main selling points for the G2 are its new software features. These are likely tied directly to LG's UI overlay and would likely not be available in a Pure Android environment.

There is also another reason LG may be holding off on a Google Edition version of the device. There are some rumors beginning to float that LG will be launching the next Google Nexus 5 device later this year with Android 5.0/Key Like Pie. According to the intel, more than likely the Nexus 5 will be built on the same hardware core as the LG G2, just as they did before with the Nexus 4 and the Optimus G. If so, it wouldn't make much sense to offer a Google Edition version of the LG G2, since it would effectively be the same device as the Nexus 5.

We will continue to watch for more intel on this subject and share it with you immediately.

Source: PhoneArena