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Lydia tends to alert enemies so I put Fortify Sneak and Muffle on her armors. Now I can sneak pretty well with Lydia beside me.

However, the wiki does not include Fortify Sneak as working for them.

So is it working or was it Muffle all along?

I think it would be muffle- I'm presuming that Lydia's in heavy armour?
Fortify sneak wouldn't reduce the noise at all, it just raises the sneak skill. While on the other hand, muffle actually reduces the sound of armour, which would help followers that have no sneak perks to sneak.
Basicly I'm saying that it's muffle because it reduces sound.