Somewhere in your mortgage contract is a "due on sale" clause. It basically means that your mortgage is payable in full if you transfer ownership of the property to someone else.
With that said, I have sold mortgaged real estate in Florida without paying attention to the due on sale clause.
The mortgage lender isn't going to know about the sale unless you tell them, or they receive a new homeowner's insurance policy sheet from an agent. In the case of your situation, that won't happen, since you'll still be living at and insuring the property.
Technically, you can't do it without permission from the lender. However, the lender isn't likely to find out unless you tell them. Also, the lender isn't likely to care as long as you keep making the paymemt.
Here's an idea: Sell the portion to the neighbor. Then, after the sale's complete, immediately refinance the property using a new survey that shows only your land. That way, you get the money for the unwanted land, and you can sleep at night knowing you have no skeleton in the closet. Plus, you can take advantage of some really good mortgage rates.....
