I'm not sure if this is going to qualify as advice but...
Your credit score will definitely take a hit when you get the mortgage and will probably take a hit when you get the car as well.
Once you start the loan process, if anything on your credit reports change, such as a new car loan, it can throw a wrench into getting the mortgage.
I have heard people say that they are going to apply for credit as soon as they leave closing because the mortgage would not yet be reporting on their reports, so they wouldn't have taken the hit for it, yet. However, I don't know if it would be possible to do that, or if it's even the right/legal thing to do. I would guess there's nothing wrong with doing something like that, but don't know.
I do know that you could request a rapid rescore or that the CRA's report the new changes as soon as they've heard from the credit that made the error when they reported to your CR's, but I do think you have to pay for that, and I don't know if you have to have a loan officer request that, or if you can do so yourself.
Lastly, I personally don't understand why people would ever want to lease a car. You pay for X amount of months, yes it's cheaper, but than at the end you've paid out "X" and you have no car. At least with a car purchase, whether new or used, you may take a hit on value of the car, but when you're done paying, you own the car and there's no more car payments until you choose to replace the car.
But that's my personal opinion, and the world would be boring if everyone had the same opinions.
