Instead, the lattice is partitioned into a checkerboard of alternating red and black sites (note this can also be done for d>2 dimensions). Can then update all the black sites in parallel (since they are independent), followed by all the red sites in parallel.
This is known as a red/black or checkerboard update.
Note that unless there is more than one site per processor, the efficiency is at most 50% since half the processors will be idle.