2001 buick lesabre keeps running hot no issues with radiator what can this be

So have the vehicle worked on

You have several issues & know that

Stop using it & have it repaired

some times when the water pump is changed you gotta fill up the radiator with coolant, run the engine until it gets hot, shut off the car and wait until the car cools down to put more coolant because some air may stay trapped inside and by following this steps you get rid of the air trapped inside.
try this:
1) when the car is cool take the cap of the radiator off and see if it's full. if it isn't, with the car still off, put some coolant until it gets full.

2) once the radiator is full, start your car and wait to see if the coolant goes down the radiator. if it does, keep putting coolant until it doesn't take any more.

Hope to be useful.

thermostat may be at fault or engine doesn't lift idle to compensate for extra load of A/C

When the motor heats up it is expanding thus stopping the leak. You need to have it checked by someone or put in some radiator dye from your local auto parts store and use a black light to determine where the leak is. Is is not hard to warp a hot engine lacking coolant and then we are talking major work to fix it. You could use some radiator stop leak found at your local auto part store such as a product called BARS LEAK which could cure the problem or make it worse by plugging the flow of coolant.You really need to know where the leak is at and get it fixed.

We would have no way of knowing your issues

You do not want to continue to use the car,
since it overheats and leaks

Have it repaired locally

maybe you have an air lock in the cooling system that would cause it to run hot

there should be a digram in front of the radiator near the hood latch or it may be on the inside of the hood of your vehicle.

The low coolant switch may be stuck, and you may even have to replace it. Last time I replaced one it was in the radiator. Also make sure the level is good in the radiator when cool.

A simple test would involve disconnecting the fan switch while the fan is on. If the fan then stops the switch has failed. If the fan continues to run remove the relay , if the fan then stops the relay has failed.
Various inputs/outputs at the relay should be confirmed to be 100% certain something strange isn't going on.
Above all be careful of the fan itself , if it's running obviously but if it's not it could start during repair

behind radiator