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"ship belonging to a shipping line," 1838, from line (n.) on notion of a succession of ships plying between ports along regular "lines." Line in this sense first attested 1786 in reference to stagecoaches. Cosmetics sense first recorded 1926, short for eye-liner. The type of baseball hit was so called from 1874 (line drive 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.