If not properly treated, how does cervical and lumbar radiculopathy progress, or does it? Could it lead to permanent damage or disability?

It depends. This is very difficult to answer as it depends on what the cause of your radiculopathies are. They do tend to resolve with time without significant intervention but there are some cases where permanent damage/disability can occur - this tends to be the more rare outcome. Your best bet is to review this with a spine surgeon, for a more detailed review.