Lucy is concerned because her family members pay little or no attention to each other. they seem to go their own way, and have little interest in even having a meal together. according to family systems theory, lucy's family is a(n) family.

Disengaged family.

Explanation:

As the exercise shortly details, a disengaged family is characterised by the lack of attention to each other, by the little interest in each other. They are withdrawn emotionally; can't gather enough interest to even share a meal together. The family system is meant to take a whole a family as a group of individuals but not picking them apart. It was first  introduced by Dr. Murray Bowen who understood that this individuals could not be understood separated from one another, but together.

a bad leader