The Castillo de Lorca is the obvious starting point — both for the views over the city and for the well-presented exhibitions on Lorca's Jewish, Muslim, and Christian past. From there, walk down into the centro histórico to see the Colegiata de San Patricio, the spectacularly tall Church of Santiago, and the elegant Plaza de España.
The Archaeological Museum is worth an hour, and during Holy Week the Semana Santa processions are arguably the most spectacular in Spain.