Your 1992 Lexus ls400 was starting fine your water pump went bad and popped the timing belt you had both replaced but the car won't start now?

It probably bent the valves. Call a dealer and ask if it is an iterference engine. If so it probably bent valves. You can run a compresson test to verify. 1992 LS400 is not an interference engine. It is unlikely that the valve train was damaged by losing the timing belt. Assuming the engine didn't run hot long enough to do damage, the timing is probably off. The timing belt needs to be checked to ensure that the timing marks are properly aligned. Ignition problems could also be to blame, but I would check timing first. Just for info, interference engines were installed late 1994 and newer.