I can't answer if the valves are damaged except to say that it's good
that the engine runs.
Overheating is not good, it may be due to the valve and ignition timing
being too far advanced (too early). Use an ignition timing light to
determine if the ignition is correct (or advanced) for the ignition is
driven by the cam - so if the cam is "off" the ignition will also be
"off" specification. If you find the ignition to be "off" specification
DON'T adjust the ignition because the error is in the cam.
Since you are doing the work yourself I suggest you turn the cam vs. the
crank by ONE cog of the belt ONLY, turn the motor by hand to be sure the
valves and pistons aren't hitting, if OK, start it. The RISK is that you
turn cam the wrong way and the valves hit the pistons which will require
removing the cylinder head and having a machine shop replace the bent
valves etc. That's EXPENSIVE! So, if you're in doubt DON'T do anything.
Have an experienced Lexus/Toyota mechanic look at the motor; he will
tell you what you need to do to make it run again.
Rather than tow the car to a shop pay the mechanic to come to the car
and look at it in your garage or yard.
I hope this helps you get driving again.