If a person had a total hip replacement (anterolatera), then what are stable leg motions?

Stable. These are exactly what their name implies; motions that promote a stable leg; and this is important especially after hip/joint replacement as part of the rehabilitative process. Ask the orthopedist/physical therapist for more about this.
Flexion type. With an anterior-type approach, the safe motions are flexion of the hip with internal rotation. Avoid hip hyperextension combined with rotation of the foot outward.
Abduction and neutra. Usually abduction, flexion and external rotation within a range. Best to ask the surgeon his/her parameters.