FX no limit scope mount , lateral adjust possible ?

The thing to try is to remount the whole thing. Perhaps swap the front and back rings, or even flip one 180 degrees.

Sports match makes ringsbthat do 4 way adjustments, but if you're running out of clicks I would think there's something else going on. I had the same issue only once and it turned out that i had somehow tightened the top of the rings before the bottoms. I'm quite sure that adult beverages may have had something to do with thst.
 
I agree regarding try to index (clock) the barrel if possible.

Or you can shim the scope base a modest amount without placing undue stress on the scope tube. Shim stock cut from a soda can measures 0.005” thick and will move the POI 3 inches at 50 yards. That’s assuming the rings are spaced about 3” apart. The amount of correction will change inversely proportional if the rings are closer together or further apart.

Note you have to shim the fixed side of the scope ring, not the side with the screw(s). My comfort limit is 3 layers of shim stock (9” of correction at 50 yards).

Beyond that, I will look at other measures like a fully adjustable mount or putting a gentle arc in the barrel.
 
I would start with making sure your scope is already optically centered. (use the mirror, etc method).

Should not have to shim for side to side (lateral) alignment any scopes unless you have a barrel/liner issue. (Vertical shimming: yes) 

Make sure that the scope and mounts are really parallel with the barrel. Not familiar with the screws/mount on the FX No Limit, but start tightening the scope mount screws EVENLY and with the scope ALREADY PARRALLEL with the barrel. It's possible that the scope was already off-angle to the left or right before as you started with the scope mount screws and it just locked that incorrect off-angle alignment in place.