Seems like this would be the best place to quote Ash from GX.
I've been playing the collection for a few weeks now on Switch, you can find my GX preview here as well as a preview discussion with prolific Mega Man YouTuber ShadowRockZX here. With that said...
...Now, as for Zero/ZX Collection: if there is any input lag, it's so minor that it's virtually meaningless, both on my 1080p LED with a Pro Controller and on handheld mode. I don't have any equipment with which to test the actual latency Digital Foundry style, so I can't back this up with numbers or anything, but just like with the classic and X collections, I have played all of these games many times over the years as a hardcore Mega Man fan (with the exception of ZX and ZXA, which I've only played about three times each) and to me they play just as well as they always have. I haven't yet taken a death in this collection due to input lag or other control issues, and for as much time as I've spent with it now during the preview phase, I don't expect to.
Does that mean your mileage won't vary? No, we're all different, but I know very, very well how these games are supposed to feel and play and Zero/ZX Legacy Collection doesn't feel compromised at all in those respects.
TL;DR - Based on my preview time with the Zero/ZX Legacy Collection (a few weeks now), I'm confident in saying that any input lag in this collection, if it exists, is minimal at best and does not adversely affect the gameplay experience at least for my setup (which, again, is a high-end Samsung 1080p LED, not a 4K display). This also goes for handheld mode, and applies across every title. I know this won't convince the usual "Classic and X Legacy Collections are trash" crowd, but hopefully this helps reassure the rest of you at least a little.