/lp user {username} group set {group} was an easy to understand addition. With its removal comes unnecessary confusion. If I were to give access to a staff member and said, "change this users group" they would look through 2 routes:

/lp group {groupname} add {player} - not a thing.
/lp user {username} group set {group} - not a thing anymore.

With the first obviously being the easiest to understand and the second being very self explanatory.
They are referred to as "groups". When you create it, you create a group (/lp creategroup, /lp group).

Using the term parent in parent set {group} to refer to group modification causes unnecessary confusion and isn't congruent(probably not the term im lookin for xD) with the actual term "group".

It would be nice if parent could be swapped out for group, or even group be added as an alias of parent to avoid confusion.

Agree with this. Not having a single letter alias is annoying. The most common command I used to do is lp u {user} g set {group}