Federated query engines allow for linked data consumption using SPARQL endpoints. Replicating data fragments from di↵erent sources enables data reorganization and provides the basis for more e↵ective and ecient federated query processing. However, existing federated query engines are not designed to support replication. In this paper, we propose a replication-aware framework named LILAC, sparqL query decomposItion against federations of repLicAted data sourCes, that relies on replicated fragment descriptions to accurately identify sources that provide replicated data. We defined the query decomposition problem with fragment replication (QDP-FR). QDP-FR corresponds to the problem of finding the sub-queries to be sent to the endpoints that allows the federated query engine to compute the query answer, while the number of tuples to be transferred from endpoints to the federated query engine is minimized. An approximation of QDP-FR is implemented by the LILAC replication-aware query decomposition algorithm. Further, LILAC techniques have been included in the state-of-the-art federated query engines FedX and ANAPSID to evaluate the benefits of the proposed source selection and query decomposition techniques in di↵erent engines. Experimental results suggest that LILAC eciently solves QDP-FR and is able to reduce the number of transferred tuples and the execution time of the studied engines.