Cement board detail
The best approach when installing cement board or other tile backer around a tub is to keep the cement board out of the lip area. Apply it to the wall with the bottom edge about 1/4 in. above the lip of the tub. Then apply a generous amount of thin-set to the bottom tile and position it 1/8 in. above the tub. Fill the gap between the tile and the tub with caulk.