Lily calls her son Mark, age 22, at least three times each day. She says she's just "checking in" to see that he ate lunch and that he's studying for his exams in graduate school. Lily is engaged in

enmeshed
parenting

Lily is engaged in PERMA-PARENTING.

Explanation: PERMA-PARENTING can be said to be permanent parenting. This is a process of raising and educating a child from birth until adulthood without end.

All things being equal, a 22 year old is no more in their childhood stage. A 22 year old is now in the adulthood stage which is a time when one is expected to take responsibility for one's own actions and well-being.

Lily calling her son 3 time each day just to "checking in" to see that he ate lunch and that he's studying for his exams" can be termed as still educating the child which is not what is expected for a mother to do to an individual adult.