Which came first the bolt rifle or lever action rifle?

Bolt action came first. It was first produced in 1824, whereas the lever action didn't go into production until 1860.

A2: The lever action Volcanic was in limited production in the 1850's. Its design was "borrowed" by Henry, and then, Winchester. There were others, like Spencer; and single-shot levers like Sharps were made during around the civil war . Levers are usually not as strong as bolt actions and can't take as powerful cartridges.