Update: the G2 is now official, and it sadly uses an IPS-LCD display
LG will launch their new flagship Android handset, the G2 on August 7th. Meanwhile, the company announced today an accessory for this phone, the QuickWindow case. This premium case includes a small window so the phone can display information when the case is closed (you'll have to swipe your finger to activate the display). LG calls the graphic interface itself QuickWindow UX, and it includes a clock, weather report, alarms, music and phone/messages notifications.
This is a neat idea, although it isn't new. Samsung offers a similar idea in their S View Cover case for the GS4. OLEDs have a clear advantage over LCDs here - as only lit pixels draw power, while in LCDs even if the rest of the display is black, the BLU unit still lights up the whole panel. So these kinds of ideas really make sense with an OLED display, not an LCD one. Is it possible that the G2 will adopt an OLED display?
Current rumors suggest that the G2 has a 5.2" Full-HD display, with very little bezel. LG have stated several times that they will not use OLED displays in their mobile phones as LCD is the superior technology for such applications (the first and only LG OLED phone was the 2011 Optimus Sol with its LG-made 3.8" WVGA panel). However they are planning to start producing unbreakable flexible plastic-based OLEDs, and these will indeed be adopted in mobile phones as they offer several advantages over LCD panels (they are lighter, thinner and unbreakable).
According to the latest information, LG will only start producing flexible OLEDs in the middle of the second half of 2013 (LG unveiled 5" panels at SID 2013), so it's probably too early to announce the first phone to use them. In addition their production capacity at first will probably be very limited so it isn't likely they will adopt it first in a flagship phone which will hopefully sell in large volume. So this isn't likely, but still, this is a possibility.
We don't have long to wait in any case, LG said they will unveil the phone on August 7th.