I am not sure on Ford but I did this on two previous GM trucks I owned. I replaced the stock open differential with an Eaton LSD and the cost was about $700 installed. The Eaton unit was about $500 and the rest was labor.
BTW, this was about 15 years ago so price might be different now.

 

I looked into it a little bit. It can be done, but I figure it will be in the neighborhood of $1000, and not an item I need right now. If you get a better idea of cost, let me know.

Also do you have the 8.8 or 9.x differential? (8.8 is more square with rounded corners, the 9.x is a trapezoid shape).