Unless I can play rhythm games with no lag, all of these are useless to me.

I never had problem playing those even on Android emulators, let alone on Linux distros.

Well, I do. For example, I can't play Rhythm Paradise (NDS) nor Taiko no Tatsujin (any console) on any emulator I've tried. It always have some form of input lag that turns the experience into a prediction game rather than a rhythm game

Don't know what to tell you - I'm playing Rhythm Heaven and Patapon, and I have no issues even on Android phone. Have you tried different devices? 

Yes, I have tried different devices (phone, tablet, an Anbernic device I have...). Don't get me wrong: I'm not saying it has a huge delay. For most games, it's so small that you wouldn't even notice. But in a rhythm game, a few extra miliseconds make all the difference. Especially if you know the game by heart (as I do).

I don't know what to tell you either, other than wondering if you have considerable experience playing either of those games on original hardware. Are you sure you are not getting some input lag and you are just taking that into account before pressing the button/touch the screen? Because I could play Rhythm Paradise on an emulator like that, but as I said, it would not be so much a rhythm game. I know the game by heart (perfected it many times), and I can definitely tell if there is any lag.

Fair enough - I'm pretty good, but not that good (my older son regularly perfects Rhythm Heaven games).

I never tried original DS version of Rhythm Heaven, so can't compare that one (again, no issues playing it via Lemuroid), but I did play both Patapon and Rhythm Heaven Fever on original hardware (and still play latter on Wii fairly regularly). Just put Fever in Lemuroid last night to check it out, played one of my favourites (Fork Lifter) and honestly man, I had zero issues (Perfect score). But I can see if you're married to particular hardware how it can feel off when you jump to different one.

Fork Lifter is a gem. My favourite Fever game is Air Rally ^^ 

Oh, I love that one.

Not as intense, but love overall vibe in this one:

Fever has really great selection of tracks.