1990 LA 360 stops running when hot (help please)

By "not start", do you mean it cranks over on the starter but does not fire, or it does not crank at all?

Can give it a shot of (starting fluid) into the air intake at the air filter or right at the throttle body butterfly. When you crank it to restart it. (open the throttle butterfly so the start fluid can get past it into the intake manifold)

If it quick starts you know the fuel pump is not pumping enough fuel, wore out or stopped all together.