Is it true that my name being on our current lease means nothing if he lived here first?
Question Details: Is this true if we file for a divorce? We have lived here for 2 years.
If your name is on the lease, you have the same right to live there as he does--actually, if your name is on the lease and his no longer is, you'd have a greater right, since a lease is a contract, and is governed by its terms. Anyone who is on the lease has the right to live there. If you divorce, in the divorce one of you may agree to move out; or the divorce court may order one of your to leave, and in doing so will look at length of residence, at your respective situations (e.g. who has a better ability to move? who has a greater need for that unit, based on disability, children, family, work location, finances, etc.). But even if the court ultimately finds you should go and not him, you can still stay there until the then-in-effect lease expires, because the family court can't override the lease, which is a contract with the landlord.
So to summarize: if you're on the lease, you can stay at least through the end of that lease. After that, it's possible a family/divorce court will order you to move when the lease expires, but it's not a given they will; the court will look at many factors, of which his length of residence is certainly one, but it's not the only one.