In this paper we study the evolution of ontology-based data access (OBDA) specifications, and focus on the case in which the ontology and/or the data source schema change, which may require a modification to the mapping between them to preserve both consistency and knowledge. Our approach is based on the idea of repairing the mapping according to the usual principle of minimal change and on a recent, mapping-based notion of consistency of the specification. We define and analyze two notions of mapping repair under ontology and source schema update. We then present a set of results on the complexity of query answering in the above framework, when the ontology is expressed in DL-LiteR.