Does lawyer have to provide me with a copy of my will that was drawn up by myself & lawyer?

Some lawyers do this to prevent you form taking the copy, signing it and then not paying for it. I personally don't, but do stamp the words "copy" on each page so that if the client does sign the will and doesn't come back to finalize the will, I can't be blamed if there are mistakes.  If you have already paid the lawyer, then you are entitled to the will, whether its a copy or a final version. 

My understanding is that your will is your property, as you paid him to draft it. If he is holding it for a good reason, like you are about to change it and leave everything to an 18 year old stripper girlfriend instead of your kids, maybe he is holding it for a good reason. If nothing like that is going on here, and he won't give it to you after you request, just go do another will with a new lawyer.