Made
popular by the song of the same
name as most popularized by the band called REO Speedwagon in the 1980's era, take on the
run means to run away, usually from a bad or uncomfortable situation.
It may also now refer to taking a food order to go, aka running with it.
He suspects that you'
re cheating, so like a coward instead of confronting the situation you leave town and take it on the
run.
I don't have time to sit down and eat. I'll just take it on the
run.