Yes give him time in therapy and see if the counselor can help him figure out why he does it and how he can change that aspect of his life. It's hard to say how much time to give him because he may need long term intense therapy to stop the lying it seems like it's common place for him now and it didn't happen over night and he isn't going to change over night. It's also up to how long you are willing to stay in the relationship and try to help him through this. he has taken the first step to dealing with his issues and getting help now you have to see the change so I would say give him a couple of months and see if there is a change, this type of situation you are going to have to play it by ear. If by several months nothing has changed and you cannot take it any longer then you can make a decision as to whether you want to stay or not.
Most compulsive liars cannot help it, if not treated it just gets worse and worse. No they don't feel good about themselves that's why alot of them do it but it's almost like something takes over them and they just do and then after they have already told the lie they usually wish they hadn't because now they have to cover a lie with a lie, it could be a mental disorder but that you will have to ask his counselor or a medical professional but it's definitely good that he is getting help for his issues now. Be patient with him and give the counseling a chance to make a difference if it can.
Then make it clear that the only way you will stay with him is if he take counseling seriously and truly tries to change and if you do not see him changing then you are gone. Think about it this way if you were the one lying and you felt you couldn't help it and then you got help only for your mate to leave you how would you feel? We are all human and make mistake some more than others but we all have done something we regret and could not take it back. If you don't feel you want to wait and see if he changes then you have to decide what you want to do maybe if you leave tell him, when he is ready to be mature and be a better person and keeps going to counseling maybe you will come back to him and tell him that you think he should work on himself and shouldn't be in a relationship right now if that is truly how you feel. The only thing about that is he may not want to wait and may find someone else in the process, that is just a chance you take when you are in love.