Jacob's lute is one of the various articles on the table inside the first chamber of the cliffside cave revealed in "The Substitute". The lute expands on the theme of musical instruments seen on the show (such as Charlie's guitar and the French science expedition's violin).
Jacob's lute is most likely from the Renaissance era judging by the number of strings used. Lutes are double-coursed stringed instruments, meaning each string has an adjacent string tuned to the same note (and often, but not always, the same octave), such as a mandolin. Jacob's lute is an 8-course lute with 15 strings. In the scene where the lute is featured, the top string of course 4 is broken and dangling from the bridge of the instrument.