As for whether monkeys will develop lumbar disc herniation, it's indeed a valuable question.
Many doctors theorize that lumbar disc herniation is the toll humans pay for evolving from four-limbed crawling to bipedal walking.
The intervertebral disc, as an organ, hasn't had time to adapt to the upright human body and is hurriedly pressed into service. As a result, it tends to prematurely wear out under heavy burden, particularly at lumbar regions such as L3/4, L4/5, L5/S1 where the stress is concentrated.
Although a monkey's spinal column resembles that of a human, there are differences, as monkeys crawl on all fours. The intervertebral disc of a monkey doesn't need to bear the burden of upright standing like that of a human. Theoretically, degeneration in monkeys would be much less than in humans.