The money factor is the lease's interest rate in disguise. Multiply it by 2,400 to get the equivalent APR — a 0.0025 money factor is about 6% APR. Dealers sometimes quote it hoping you won't convert it, so always do. Like a loan rate, it depends on your credit and can sometimes be negotiated.
The residual value — the car's projected worth at lease end — is set by the leasing company and largely fixed, but it drives your cost: a higher residual means less depreciation and a lower payment, which is why cars that hold their value lease well. The most negotiable number is the capitalized cost (the negotiated price): lowering it reduces depreciation directly. Focus your negotiation there and on the money factor, not on the monthly payment in isolation.