Mom has severe osteoarthritis in spine. Had cerv. Laminectomy. Lumbar surgery to put rod in recommended. Consequences of no surgery?

Symptoms. Pain, bone collapse if osteoporosis if cord pressure is involved- paresis or paralysis.
Depends. If a rod is needed (a fusion), then there must be some type of deformity, instability, or disc height collapse present which needs to be treated at the time of surgery. As far as the consequences of not proceeding with surgery, you and your mom should have a talk with the surgeon to understand what the non-surgical long term outcome would be for her specific problem.
More pain. Arthritis is a progressive disease---gets worse over time. Treatments may slow down the progression, but we are all subjected to the effect of time. Since her disease is severe, she was advised to have the surgery done--the likely reason is to help stablize the spine....Minimize risk of collapse. Should ask the surgeon about pros/cons of the procedure.