I would like to know how to make the headlights turn off when you turn off the car instead of staying on for several seconds

I am not sure for your Lexus, however, My Cadillac timer for the delayed headlights is a knob surrounding the head light switch. You can adjust the time from (0)off, none to a few minutes. It looks similar to the dash light dimmer knob.

Yours: Grumpy

Check with you local dealer as there is probably somewhere you can adjust the settings.

look for fuse daytime running lights or auto