Complex sentence: In the few years following, the Kallets bought the Star and the 1907 Lyric, which had been showing films intermittently mixed with live programming under various names--first the Lyric, followed by the Family, Regent and finally renamed the Family again.
Split into simpler sentences: In the few years following, the Kallets bought the Star and the 1907 Lyric. It had been showing films intermittently mixed with live programming under various names: the Lyric, followed by the Family, Regent, and finally renamed the Family again.