1990 LA 360 stops running when hot (help please)

Replace the ballast resistor first followed by the ECU box.

Most likely is the ballast resistor has failed and has a crack in the windings on the primary start circuit that becomes seperated with heat. However, the ECU could have a similar issue.

It’s cheap to just replace both and will likely fix it for little cost. 30 year old electronic parts are probably due to get replaced anyway.