"fail to keep pace," 1520s, earlier as a noun meaning "last person" (1510s), later also as an adjective (1550s; e.g. lag-mon "last man"), all of uncertain relationship, possibly from a Scandinavian source (cf. Norwegian lagga "go slowly"), or some dialectal version of last, lack, or delay. Related: Lag; lagging. The noun meaning "retardation" is from 1855. First record of lag time is from 1951.
A convict: lags who escape from the county pokey (1930s+ Underworld)
To arrest or imprison a criminal (1940s+ Underworld)