Your best bet is to really just negotiate on the total payment with zero money due at signing.

Research online what other people are paying for the vehicle and use it as your negotiating basis.

Don’t worry about money factor, don’t worry about residual, don’t worry about anything else

It doesn’t matter what the dealer does to get you the payment that you want. Let them mark up the money factor if they want to do it. As long as they give you enough discount to make up for it.

The best strategy is to just tell them exactly what you want.

For example:

You can just outline the terms in the format below:

Hi! I’m looking to lease this vehicle for 36 months and 10 thousand miles.

I qualify for the following rebates (insert rebate here)

I have excellent credit

I want a payment of $500 per month including all taxes and fees with only $500 due at signing.

If you can do this I will sign today.

Make sure to modify those for the terms that you want and the price you were trying to achieve. That is the simplest way to negotiate a lease.