Is having a lack of empathy a sign of mental immaturity?

Possibly: It could represent lacy of maturity or it could represent a personality disorder.

Yes: Sometimes people take a very long time to mature--and they may not ever. Such people, with a "fixed" and more primitive psychology are likely to be diagnosed as having a personality disorder--a purely descriptive term. A psychodynamic view is that pervasive childhood suffering, maybe subtle, causes the personality to arrest. Lack of empathy suggests a very young childish self-centeredness.

Empathy: It is a sign of limited interpersonal skills which in some sense could be labeled interpersonal immaturity or of a self centered relational style. Best.