I have the same dilemma, and asking around, it seems that you need to dig out some of the existing mortar to have enough depth for a new layer to stick. My own fireplace has very deep mortar to begin with, so I'm not sure I'll need to do that, but I do plan to clean it with some kind of acid wash to get the surface ready. Your mortar looks fairly near the surface. You might first look at Rumabio lime wash products which can re-color both the stone and grout with much less investment than a re-grouting project.

Replacing the wood paneling would also help to lighten the dark room.

Just wondering if you’ve done anything yet. I have a similar fireplace I’d like to lighten.

Not yet @Joan, thinking of following the blog from Chris loves Julia.

Funny thing. I just posted on another discussion with the opposite dilemma. Someone purchased a home where the grout had been painted white, and they don't like it. You should look at that post here: Fireplace Delemma

To lighten up the room, you may consider whitewashing the stone rather than changing the grout.