Can a old injury from a strained ligament cause your patella to be tilted laterally?

Yes. One component that can affect the patella tracking down the middle of what is known as the trochee at groove in the femur is the balance of the medial and lateral Ligaments that attach to the patella. So if the medial ligaments have been injured and did not heal correctly, it may cause an abnormality in patellar alignment and tracking.