After 10 minutes on a threadmill I start feeling pain in the left hip joint (also muscle numbness) and have trouble lifting the left leg. Why is that?

Joint, bursa,tendon. It depends where the pain is. A lot of hip problems are bursitis and tendonitis but they can be joint as well. You evalaution will include a history, physical and imaging including x-rays, ultrasound and/or mri.
Back versus Hip. Overuse of an arthritic joint can cause pain especially after exercise but numbness and muscle pain can be signs of nerve compression in the lower spine level. Suggest getting both checked by a physician with expertise in musculoskeletal disorders like a rheumatologist, orthopedic or sports medicine.
Nerve impingement . Your history suggest that your symptoms may be coming from the low back/ lumbar spine. Recommendations for further work up and treatment will need to come after a thorough physician consult.