I'm trying to make sure I've got the LUA logic down on this topic.

I know that when you add wallkers to a map, you have to edit these lines in the LUA: So since AT-TEs have three pairs of legs, you change the zero in (3, 0) to the # of walkers, so (3, 2) for 2 AT-TEs.

My question is: if I want to have 3 AT-TEs and 2 spider walkers, should my LUA lines look like this? If not, what would I need to make them look like in the LUA?

That should be correct. A good way to always make sure is to test it out in-game.