told me that he is no longer willing to support me using Ativan. I asked him about a weaning schedule for it as I don't really want to be on it anymore either and he's saying that I cut one full pill every 15 days.
Unfortunately, this is a classic example of why benzodiazepines shouldn't be used as primary, taken daily meds for anxiety. You never know when your doctor will pull the plug on them and then expect you to get off them quickly. Even worse, IMHO, he's now expecting you to wean off Ativan just as you start taking a new antidepressant which is the very time you may need it most.
Cutting back by one tablet every 15 days is probably doable given you've been on Ativan for a relatively short time, but stopping it while starting the Cymbalta may increase the degree of difficulty quite a bit. I'd dig my heals in on this and if your GP isn't willing to delay the Ativan discontinuation until you're stabilized on an effective dose of Cymbalta then ask to be referred to a psychiatrist if this is possible.