It don't? That's weird because I am able to use microtype package with XeLaTeX.

Ohhh I see, I look it up. Apparently, it support specific feature[0] of microtype in XeLaTeX.

[0] https://tex.stackexchange.com/questions/118713/is-microtype-...

That's not clear from the document. I couldn't find a clear statement. What about LuaLaTeX?

It works fine with LuaTeX, in my experience. (And the document does make it clear: see Table 1, on page 6.)

Does fontspec work with LuaTeX?

Yes, it does. In general LuaTeX supports everything that XeTeX does.