that happend to me and the fix of this problem is ( you must get the new update for your vedio card )
That graphic problem is also one of my problems when I first time play LU. Yes, 32 bits solved the problem, now I can play with no lines or something like that.
The Video Card required to play GTA III is:
Nvidia GeForce 2 MX 100/200 32MB / ATI Radeon 7000 64mb or more.
I hope this information helped you.