LG is not behind in making 1080p display device, according to GLBenchmark LG is coming up with new device model named F240 with 1080p display. Unannounced LG F240 smartphone houses Adreno 320 GPU, Android 4.1.2, and 1.5GHz processor (probably Qualcomm Snapdragon S4 Pro). But htis is not currently confirmed but put your thoughts on an LG device with a 1080p display.
Additonally, Samsung has started building 1080p AMOLED Displays. If benchmarks above are true than we might see LG F240 at CES 2013.
VIa: Phone Arena