I signed a lease a few months ago and someone from the apartment signed it as well. The move in day is in august. Now, they are saying that my lease is not “fully approved” and I can’t move in until I send in my proof of income. By saying I can’t move in, I feel as if they aren’t fulfilling their obligations of the signed lease. I would like to get out of the lease and I am wondering if it will be easier to do since at this point I am not fully approved.
A lease is a contract. A contract becomes binding once there is an offer and acceptance. Sometimes something smells like an offer, but it is really an "invitation to treat", a sign that they are willing to negotiate. The clear sign that they did not make an offer (as required for there to be a contract) is that they do not consider themselves bound the minute you accept. The language of the document would include some provision like "subject to approval of the application".
It is possible that you have "made an offer", which they can accept thereby completing the offer-and-accept cycle, but until you do, you can revoke your offer, if you really want out. You do have to clearly and quickly communicate the revocation.
Not once you have a lease
It's not clear whether you do or not and it will depend on the particular circumstances.
One possibility is that you have entered a binding lease, and the requirement that you provide proof of income before they will give you access is a term of that contract. If so, your failure to do so, while probably not a breach of the contract, means they are justified in refusing access. The consequence of this is that you are liable for the rent even though you cannot access the property - they can't be made to suffer loss because of your actions.
The other possibility is that the acceptance of the contract is conditional on "final approval" (whatever that is). At this point, you do not have a lease, but if you have allowed them to incur losses (such as not renting it to someone else) by a promise to provide the information you agreed to, and led them to believe you would provide to get "final approval", then they may seek damages under the doctrine of estoppel. At least in australia, where estoppel may be used as a "sword" and not just a "shield" as is the case elsewhere.