A baby born to one or more crimminals; to have a parent who was convicted of a crime; a baby born to a mother who gave birth while imprisoned; a baby born to a fugitive of the law.
"on the runbaby, conceived through a crimminal"
--Llyod Banks
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.