Hello from JustAnswer.
It is very rare that degenerative arthritis or degenerative disc disease of the lumbar spine will result in paralysis. It is possible that it can happen and it is the worst possible complication of the disease process, but the likelihood is quite low.
In addition, if the condition worsens and there are some early neurologic symptoms, then your doctor can implement treatments that can ease the neurologic symptoms and reduce the risk of subsequent paralysis.
If i can provide any additional information, please let me know.