The LX for 1990 is coded WR650D, and Yamaha covered it in LIT-18616-00-52. That manual reaches across the 1988, 1990 and 1991 model years and also documents the Wave Runner and the Wave Jammer.
Three related craft in one volume, which is how Yamaha handled this period. The LX sits alongside its siblings rather than in a publication of its own, and the procedures note where it differs.
For the work itself, expect the factory's torque specifications and service limits, disassembly and reassembly sequences, the wiring diagram, and diagnostic procedures for engine, fuel, electrical and propulsion faults. None of it is written to impress; it is written so a technician can finish a job correctly.
Confirm WR650D on the hull plate first. Components from neighbouring years interchange more often than the paperwork suggests, and the code is what settles it.
