Where does the term “on the Lam” originate?
See: http://www.takeourword.com/et_k-m.html#lam
and I quote:
Lam, as in on the lam, first appears in 1897 and comes from the verb lam which means run away.' It is of unknown origin, but sometimes attempts are made to connect it to lam beat,’ as in lambaste. This connection becomes clearer if one considers that beat it also means `run away,’ and one source indicates that this meaning of beat it is Old English. I have seen nothing to substantiate that, however.
I thought it was “on the lamb”, referring to beastialic, pedophillic shepherds. 
Wrong thinking is punished, right thinking is just as swiftly rewarded. You’ll find it an effective combination.