L hip and leg pain when lay on my r side but no l sided pain when I lay on my l side. Why? Thank you.

Radiculopathy. Your symptoms may reflect a lumbar radiculopathy (radiating pain due to a pinched nerve in the lumbar spine). In many patients, certain positions can cause increased irritation of the pinched nerve, which can lead to increased pain. See a physician for further evaluation/treatment if symptoms persist.