To support reactive and predictive applications, complex event processing (CEP) systems detect patterns in event streams based on predefined queries. To determine the events that constitute a query match, their payload data may need to be assessed together with data from remote sources. Such dependencies are problematic, since waiting for remote data to be fetched interrupts the processing of the stream. Yet, without event selection based on remote data, the query state to maintain may grow exponentially. In either case, the performance of the CEP system degrades drastically. To tackle these issues, we present EIRES, a framework for efficient integration of static data from remote sources in CEP. It employs a cost-model to determine when to fetch certain remote data elements and how long to keep them in a cache for future use. EIRES combines strategies for (i) prefetching that queries remote data based on anticipated use and (ii) lazy evaluation that postpones the event selection based on remote data without interrupting the stream processing. Our experiments indicate that the combination of these strategies improves the latency of query evaluation by up to 3,725x for synthetic data and 47x for real-world data.