Replacing an engine (engine replacement) is not the same as an "engine change", and does not require a Smog Check Referee inspection.
In this case it appears you've conducted an engine replacement, and not an engine change. You may proceed to a standard smog check station, either STAR certified or regular, depending on which the DMV has required.
The BAR refers to an engine change only when a different model, year, make of engine is installed in a vehicle which it was not originally designed for. Since the engine you've used was built for your Lexus LX450, the repair is considered a engine replacement and not an engine change... normal smog check, just as if the repair you made was something minor to an emissions component.