"vessel belonging to a shipping line," 1838, from line (n.) on notion of a succession of ships plying between ports along regular "lines," as distinguished from transient ships using those ports. (Line in this sense is attested by 1786 in reference to stagecoaches.) Earlier it meant "man of war, ship of the line" (1829). Meaning "cosmetic for highlighting the eyes" is from 1926. The type of baseball hit (forcible and parallel to the ground) was so called from 1874 (line drive is attested from 1899).
"person who fits a lining to," 1610s, agent noun from line (v.1). Meaning "thing serving as a lining" is from 1869. Liner notes in a record album are attested from 1953.