"flight," as in on the lam, 1897, from a U.S. slang verb meaning "to run off" (1886), of uncertain origin, perhaps somehow from the first element of lambaste, which was used in British student slang for "beat" since 1590s; if so, it would give the word the same etymological sense as the slang expression beat it.
on the lam, take it on the lam
[1886+ Underworld; ultimately fr British sense ''beat,'' found by 1596, hence the same semantically as beat it]