Some site mention GTA:LCS can't play on the PSP 1.50, while that is not true.
From PSP 1.00 or 1.50, all support AVC but only to the UMD(Video) or GAME(Cut Scene).
You can try PMF Player, put the GTA:LCS Title.PMF on to the PMF Player with a PSP 1.50 it will play the video corrently.
So that, there is other reason that GTA:LCS can't on the PSP 1.50. Not because of AVC codecs.