It doesn't make any difference to the dealer how you'll finance the vehicle.
Chase has very good buy and lease rates - at or below anything third-party.
If you want current money factor Edmunds is a good source, they'll also report current residuals per model and mileage allowance.

We got 2% on 36/10 lease, 63% residual. If you walk in and don't know what the rate is then sure they'll try to bump to make up some profit dollars.

If you have third party financing in many cases your dealer will meet or beat the rate. Or they'll give you a 5-day option to transfer your contract to your finance source - you drive-off on theirs.

I've been buying and selling cars for forty years, sold for a year, BIL sold for 15 years - I know how it works. If anyone needs help with negotiating I'm happy to help where I can.

This was our third purchase from this dealer and they still started a hundred a month high on the payment. When I balked and asked for lease terms they then just asked where I wanted to be - I told them, and we ended up very close to that. But you have to know what the rates and invoice, and terms are or they'll try to stick you on the payment. Even a modest bump in rate adds a few hundred in profit to their deal. Or under-allow on your trade, or get you to put more money down - all ways to build profit in the deal. Next finance will try to sell you a bunch of add-on crap of which none of it is worth it, but it adds to their profit by tacking on 'just a few dollars to your payment'. Sure. :D