LookAt Translation Not Sticking

I took my dampened lookat code from a post, but I'm still having trouble.

I use A/D to let the player rotate my ship along Y. In addition, after I select a target and hit T, the dampened lookat will turn the ship like it's supposed to. But, if I use the A/D rotation after the lookat, it snaps it back to the original rotation. Moving foward does not snap it back and it behaves the same whether or not I use localRotation or rotation. This is all in Update().

Any ideas?

     // Y rotation only
     if (Input.GetKey (KeyCode.A)) {
         shipY -= turnSpeed * Time.deltaTime;
         transform.rotation = Quaternion.Euler (0, shipY, 0);
     } else if (Input.GetKey (KeyCode.D)) {
         shipY += turnSpeed * Time.deltaTime;
         transform.rotation = Quaternion.Euler (0, shipY, 0);
     }
     // Warp
     if (Input.GetKey (KeyCode.T)) {
         if (warpTarget) {
             var neededRotation = Quaternion.LookRotation (warpTarget.transform.position - transform.localPosition);
             var interpolatedRotation = Quaternion.Slerp (transform.localRotation, neededRotation, Time.deltaTime * turnSpeed);            
             transform.localRotation = interpolatedRotation;
             shipY = transform.rotation.y; (this line doesn't fix it either)
         }
     }