It's a shame nobody's replied so I'll put in my 2 cents, and that is, next time I'd let your local mechanic do the radiator replacement. But since it's a done deal and the radiator's already fixed, there's nothing wrong with letting real Lexus techs do the job but unfortunately you did pay too much! It doesn't take a certified tech to change a radiator nor any of the other repairs they did. The only wrinkle in cooling system work I can think of, is that Lexus says that "burping" the cooling system is a must (at least it does for my 2017 LS). And there is supposed to be a screw on the upper radiator hose connector that you loosen during the process while the engine is running just to let any air out of the cooling system.
I realize there was not much you could do about the past owner's neglect, because for the radiator to rust out might mean the owner never changed it. Also you obviously didn't expect everything to be completely trouble free on a 200,000 mile car! But for next time, I'd do a drain and fill with distilled water plus Lexus OEM coolant (which they do actually sell as 100% type coolant instead of using that 50/50 "universal coolant" dreck that's just a rip off). The distilled water will be effective in the cooling system for a lot longer than the tap water that most of them use for coolant changes.
My jiffy lube I go to for oil changes, offered me their cooling system service for $100 or something. I said I'll do it, but I have the coolant I want you to use plus the distilled water because I don't want your cheap universal coolant from a dirty 50 gallon drum. They said nothing doing! So now I'm still looking for another mech that will do it my way.
