In my review of Mega Man X Legacy Collection, one thing I wasn't sure about calling out was the possible presence of input lag. I didn't have the proper tools or setup in order to gauge such a thing, and I didn't want to call such a thing out without being absolutely certain it was the game and not me.
So while I couldn't "jump rope" with Vile's punches at the beginning of Mega Man X as well as I could in the past, I didn't really notice anything hindering my performance otherwise. As such, I figured it best to wait until someone better equipped to tackle the issue did so -- and that time is now.
GigaBoots has a pair of videos on the subject, the first comparing the new collection to the Super Nintendo Entertainment System originals (with a different controller), and the second comparison looks at Mega Man X Legacy Collection against the PlayStation 2's Mega Man X Collection and the Super NES originals with a standard Super NES controller:
There's more to come with testing the Nintendo Switch version of the games, in which they promise something "interesting" about it.
For what it's worth, to reiterate: Some measure of lag is almost to be expected when playing vintage games on high definition televisions with wireless controllers, but even then, I didn't really notice any major problems with lag when I was playing, except when I was trying to do something that was already extremely difficult to pull off (the Vile thing). So unless you're a really high level player of some sort (or just really sensitive to lag, as some people are), I don't think this should affect your enjoyment of the games all that much.
But maybe you disagree? Feel free to share your thoughts and experiences in the comments below!