Can cervical spondylosis, if left untreated, cause lumbar spondylosis?

No: Cervical spondylosis has nothing to do with the lumbar one. Both can co-exist, though, but none is caused by the presence of the other.

No: Cervical spondylosis means the spinal canal is narrowed in your neck and lumbar is similar in the lower back. They can be associated because patients who develop arthritis or narrowing in the neck may have the same systemic pathology (ie arthritis) in the lower back, but they are not directly linked. In other words, cervical spondylosis does not lead to lumbar spondylosis.