Could lower back pain that radiates around hip to 4 1/2 month iguinal laproscopic hernia repair be olioiguinal nerve pain or reoccurrence ?

Could be: Inguinal hernia recurrence is possible, and needs exam to be certain. If there is no bulge, unlikely. Neuropathy can occur and may fade with time, or may need nerve block if painful. If numb ignore and the nerves will slowly fill in. Lower back pain could be from bad posture, slipped disc etc while not moving well after operation.

Doubtful: While it is possible, it doesn't sound like that type of pain. Ilioinguinal nerve is also well away from the space where a laparoscopic inguinal hernia is. It could come in to play however if a tack was placed too deeply at the upper outer edge of the mesh. See your surgeon to find out if its bad enough. Recurrence would be more likely if there is a return of preop symptoms or a reducible bulge.