Do I need to cut the bottom row of tiles for a shower wall to keep them level?
I do not set the bottom row first. I  start with the second row and tile on up.
I use a ledger board ( a straight furring strip or 1x2 ) at the correct height so that the bottom of the tile of the second row is slightly lower then the height of the tile that will be the first row. You need to figure out the  correct height to place your ledger board.   Make sure you do not leave to big of a space, check all around the perimeter. Use a level to mark that line so you can place your ledger board level.
Doing it this way insures that you start level, plum and true. ( because the lip of your tub is not ) Hopefully your walls in the corners are plumb and true but they frequently are not. ( make sure you do not leave a sliver of a space to fill at the corners )
The next day when the tiles are set you remove your ledger board and do the bottom row, custom cutting the bottom of each tile to match the angle of the tub lip and leaving a small gap for caulking.