My mom was diagnosed with lymphedema. How serious is this condition?

Depends. The answer to this question depends on the cause of the lymphedema. Many forms of lymphedema are secondary to some other problem. Once the primary problem is resolved then the lymphedema is resolved. It is best to seek the opinion of a physician with special interest in lymphedema.
Varies. It is difficult to walk the worse the lymphedema becomes and with inactivity the area can ulcerative, leak and possible become secondarily infected. Movement is important stair stepping with support will help, as well as enzymes - bromelain, serrapetase or wobenzym.
Lymphedema. this is a chronic condition, and requires daily use of a compression stocking to prevent worsening of the swelling. additional therapies include manual lymphatic decongestion(MLD), or a lymphedema pump, however stocking are the main need.