If I lease my house, can I file for a chapter 11 bankruptcy right away and get a "cram down" on my mortgage? (The house is way underwater.)

If the house is your principal residence, there is no way to force the lender to accept anything other than the current contract terms.  Even if it is not your principal residence, the lender has the right to do what is known as "an 1111(b) election" to require the full amount of the loan to be paid, although you can usually stretch it out over a longer term and reduce the monthly payments somewhat. Leasing just before filing bankruptcy might work to change the character of the property from  principal residence to rental.  But that is going to ultimately be up to the Judge in your case.   Chapter 11 is very complex and involved, but the bottom line is that it is all about negotiations with the creditors.  If you can get your creditors to agree to whatever you are proposing, then you can usually confirm a Plan of Reorganization.   Be sure you hire an experienced bankruptcy attorney if you proceed.