I would imagine that a mere delay before switching on the lights is impractical.
Imagine that your battery is already flat, or very nearly so. There may only be enough oomph left in it to actually crank the engine.
Better I would think to take a voltage measurement from the battery supply, and trigger the light switch at say 14.5v, that way the lights can only come on automatically after the engine is running.
I suppose there are other ways to achieve this too, for example you could monitor the output of the crank sensor, assuming the engine/ car is young enough to have one, and switch the lights on when crank speed reaches say 500-600 rpm. Easier though I would think to just monitor the battery voltage threshold.
Use that method in combination with a supply, like the one for the radio as suggested, to switch off the lights again after a small delay period has elapsed.
rgds