transform.lookat in right direction

Hi i want do do exactly what lookat does except on the right vector point. So how do i Rotate the transform so the right vector points at target’s current position. also my x and y rotations are frozen so i cant just lookat then -90 on the y.

Just set transform.right vector manually.
Something like this:

transform.right = (pointYouAreLookingAt - transform.position).normalized;

Adjust other angles after setting this vector in necessary.