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.