LSD or not?

Use an impact wrench (I think it's 22 mm) and it should be OK

 

I’ve yet to hear of anyone who damaged the threads getting a 22 mm plug out. Just make sure you open the fill before drain and have new plugs to replace the old ones. Spray it down with PB blaster for a few days to put your mind at ease.

 

Looks like your rear diff could use a good power washing/wire brush, and a fresh coat of Rustoilum paint. Every new to me truck I get I thoroughly check the frame and diffs, do a light sanding and spray paint them with anti rust paint once yearly--as I live in a state that gets snow. Helps them last longer.

 

LMFAO!!!

 

That thing needs a hammer and a die grinder with a wire wheel attachment to make it decent enough to paint with a rust encapsulator.

 

Poor OP
We want pics of drained fluid and magnet when you get there!

 

Also a New Englander here. That rust is really bad... I would do something about it this weekend -- seriously! It's so easy to treat it before it starts leaking, and nearly impossible after it starts leaking. If you ignore it I would expect the diff will be leaking by spring.