My landlord gave me a copy of the lease with his signature only. The copy I signed is not in my possession. Is this binding? Will it stand up in court or should I ask for a copy of the lease with my signature?

If you signed the lease and the landlord signed it it is binding. The only thing that may not hold up is of there are handwritten changes that you didn't initial.

Whether the landlord is required to give you a copy may depends on local laws (ANY question on law needs to include your general locale as laws vary by area. ) But you can definitely ask for one.

You can ask for a copy but the lack of one in your possession does not make his copy void. Why do you ask, are you trying to get out of this lease?