It stands for Lactose containing APT broth. APT broth was developed by Evans and Niven, 1951. Shahani and Vakil, 1962 might have been the first to use it with added lactose.

Thanks Robert, but the LAPT media I am using doesn't contain lactose.

LAPT broth: 1.5% Bacto Peptone, 1% Bacto Tryptone, 1% yeast extract, 1% glucose and 0.1% Tween 80