Interaction of cytoskeletal filaments, motor proteins, and crosslinkers drives important cellular processes including cell division and cell movement. Cytoskeletal networks also undergo nonequilibrium self-organization in reconstituted systems. An emerging problem in cytoskeletal modeling and simulation is spatiotemporal alteration of the dynamics of filaments, motors, and associated proteins. This can occur due to motor crowding and obstacles along filaments, motor interactions and direction switching, and changes, defects, and heterogeneity in the filament lattice. How such spatiotemporally varying cytoskeletal filaments and motor interactions affect their collective properties is not fully understood. We developed the Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) for problems with significant spatiotemporal variation of motor or filament properties. The simulation builds on previous work modeling motor mechanochemistry into a simulation with many interacting motors and/or associated proteins. CyLaKS also includes detailed-balance in binding kinetics and movement and lattice heterogeneity. The simulation framework is flexible and extensible for future modeling work. Here we illustrate use of CyLaKS to study long-range motor interactions, filament heterogeneity, motion of a heterodimeric motor, and how changing crosslinker number affects filament separation.