LG Display's CEO Han Sang-beom said that the company plans to start mass producing flexible OLED panels in the second half of 2013. He wouldn't say whether they got any orders for the next-gen flexible panels, but obviously there are speculations that Apple is behind those orders. It's probably unlikely as capacity at first isn't likely to be enough for Apple.
This actually marks an expediation of LG's flexible OLED plans. In January 2012 the company said that they will start constructing a new pilot line in Q3 2012, which will become active by the end of 2012 and the company will need 1-2 years to develop and verify the process before producing at mass volume.