1. A method of operating a lower level cache memory of a data processing system, comprising: receiving, by a store queue controller, an operation that is associated with a first thread; and using, by the store queue controller, logical partition (LPAR) information for the operation to limit dependencies in a dependency data structure of a store queue of the lower level cache memory that are set and to remove dependencies that are otherwise unnecessary, wherein the operation is a synchronization operation and the using further comprises: setting, by the store queue controller, dependencies in the dependency data structure of the store queue of the lower level cache memory for the synchronization operation to store operations not on the first thread with LPAR information that matches the LPAR information for the operation.