A lease in joint names is NOT a solid requirement, but it's one of those pieces of evidence which is helpful. There is no certainty that you will be granted a visa, and I imagine you will have to argue your case quite hard, but the matter of no lease doesn't rule it out.
Keep collecting evidence. INZ commonly require more evidence (covering the processing time) just before the visa is issued. You will also need to use some of this evidence all over again when you are in a position to apply for Residence, so keep copies in case of some not being returned.
You may have seen these old threads
https://www.google.co.uk/#q=site:enz...tnership+proof which have discussion and more ideas about partnership evidence.
You will probably have seen that you need to account for time spent apart, so INZ will probably want proof of your work, and of your partner's student status.