I noticed this with a modded Lydia I use as well. I made a new companion from scratch, gave her some armor and when I first saw her in game she was naked/in underwear (depending on if you have a replacer or not).

I gave her armor. Why isn't she wearing it? Bug? Workarounds?

Did you simply put it in her inventory or did you give her an outfit? I don't think NPC's equip inventory items, so you must give her an outfit for her to be clothed.

Good point. I'll check tonight.