A couple of the ladies here have shared their experience with having a formal separation agreement drafted. It usually spells out in specific terms, residence, child support and yes, dating (usually prohibited if reconciliation is a possibility at the time of separation). Now as to whether or not the lies stop, I don't know. I sure hope so. They are as debilitating and destabilizing as the infidelity itself. My husband told me this week that ending the lying is the hardest part for him (was that a lie? sorry, can't resist that inappropriate joke).
Therapy is the first step. An unwillingness to work on getting better is a dead end. Best wishes.
Wife of a survivor