My husbands applying for Legal Aid in Ontario. They want to put a lien on my house. Will that lien come off my house after the case is finalized?

Who is they? Legal Aid?
A lien generally is taken off when a debt is settled. It isn't automatic - sometimes the lienholder has to be reminded.

Something does not sound correct about this. Legal aid, normally does not do liens, but if an attorney is wanting a lien to do legal work, that means he will want payment. So it sounds like, no, the lien will remain till some amount of money is paid.

The case won't be finalized until they get PAID.

Since you aren't answering back, have your husband ask the legal aid people to explain liens. You haven't even said in what respect it is 'your' house, when he is your husband... You can't ask legal questions with so much lack of detail.