http://www.neoya.com/wii2hdmi
you'll be no more lagless with a wiiu than this.
it's more than likley your display casuing the most of the lag.
If its not your display (i.e you have a really good one) then the adapter isnt going to create any more noticeable input lag
I have a Wii connected through composite to a CRT for Project M. That is lagless.
I have a Wii U and the official gamecube-adapter running HDMI for Smash 4. That is also lagless.
I already have the equipment and it works perfectly for Melee on Wii U (through Nintendont). That is also completely-lagless. Project M also runs completely-lagless on Wii U. The problem is the controller.
I very much would not like to spend $30 for an adapter to a console that might very well die out if P:M gets support for the controller-adapter. I have a lot more faith in P:M than some weird one-use adapter. I could probably buy a whole Gamecube/CRT-setup with a controller on Craigslist for $30 (I've seen that price around my area).
The moment I can play Project M on my HDTV with a Gamecube controller and the official adapter is the day I pack up my Wii and CRT to become exclusively an additional tournament-setup.
The only thing restricting Project M on Wii U is the controllers, and this thread shows that there is at the very least SOME demand. Once that's incorporated, P:M will run the same as most all original Wiis.
Who knows, maybe the Wii/Wii U homebrew-scene can make it work with other Wii games running in vWii that use the Gamecube-controller, IE Mario Kart Wii.
Frankly, this could also help those unfortunate souls stuck with the Wii Family-edition to play Project M as intended, God bless those poor people (Mini users RiP). That scenario would also lead to more adapter-sales from Wii U-holdouts.
This might even lead to bigger things than just P:M.
I know it's not a competitive-thing so it's not a priority, but I can hope, right?
At least there's always that awesome addon-system! P:M 3.5 FTW!