Lazy replication is a popular technique for improving the performance and availability of database systems. Although there are concurrency control techniques which guarantee serializability in lazy replication systems, these techniques may result in undesirable transaction orderings. Since transactions may see stale data, they may be serialized in an order different from the one in which they were submitted. Strong serializability avoids such problems, but it is very costly to implement. In this paper, we propose a generalized form of strong serializability that is suitable for use with lazy replication. In addition to having many of the advantages of strong serializability, it can be implemented more efficiently. We show how generalized strong serializability can be implemented in a lazy replication system, and we present the results of a simulation study that quantifies the strengths and limitations of the approach.