Will an ACL in the knee heal on it's own or repair itself?

Probably not. A complete tear of the ACL never heals itself. Most but not all will require some form of reconstruction. .
Rarely. A full thickness acl tear very rarely repairs itself. Acl reconstruction is recommended for younger and athletic patients. Middle age and older and/or more sedentary patients without major instability symptoms can do well with rehab instead of surgery. Partial acl tears have a greater healing potential.