This is definitely supported.
First, go into the existing AP group, open the AP settings and then save the AP system profile as a new name (Save As is at the top of the screen). That way, the existing AP group will utilize a unique AP system profile (not the default).
Then, create the new AP group and open the AP settings. Save that AP system profile as a unique name as well.
Now, each AP group has a unique AP system profile.
You can then make the LMS IP changes without affecting the other AP group(s).
Make sure you use the IP associated with the "controller IP" (on the first configuration screen of each controller OR "show controller-ip") in the LMS IP field.