Front derailleur rotates on frame

[aicabsolut]

If you're certain the L limit is correct, then another reason it may not shift to the small ring is that your cable is too tight.

Check the tail end of the cage alignment in the big ring little cog combo.

Then check for chain rub when you're in the middle ring and large cog. If you get chain rub on the inner cage, loosen the cable.

If there's no rubbing in the middle ring, then shift to the small ring and large cog and check your lower limit. If that's ok and it's still slow to shift to the little ring, loosen the cable tension and try again.

Again, if the clamp is loose, I would expect there to be more than just a lateral shift going on. The cage would most likely also drop down lower due to downward tension from the cable coming up from the BB. Then you wouldn't be getting enough clearance over the big ring either.