You sure it has lag?
I game on a Sony GDM-F520 which supports 1536p but only got 0.3 frames of lag when testing (taking human error into account that basically means 0).
Okay so after doing more research it actually depends on the TV itself. Some HDTV CRTs will upscale 480i/480p signals to 1080i which will add lag. And some of them have post-processing effects which add a lot more lag (some you can't turn off).
The monitor I have has none of those.
So I would recommend getting an SD CRT for Melee, or better a PVM or BVM monitor for the best picture quality.
I have two Sony GDM-F520 too, they are excellent and do not have any lag*. They are, however, no HDTVs. They are PC monitors and, as such, do not have any of the laggy post-processing that HDTVs have (since PC output is already in the high standard of progressive RGBHV that CRTs ideally require).
I was referring to HD TVs usually having lag. PC CRT monitors are no subset of these, so naturally I was not implying that CRT PC monitors had lag.
*Most GPU RAMDACs have a delay for the analog output over digital outputs of 0-1 frames. For Wiis and Gamecubes set to 480p60 output, this is no problem since they output digitally from the start.
Edit: Here's a first-hand experience from somebody who had an HDTV CRT that lagged quite badly:
https://www.reddit.com/r/smashbros/comments/2zliks/lag_on_a_widescreen_hd_crt_melee/cpk3gqc
I personally don't want to ever buy one of these. They are heavy, rare in Europe, hard to get rid off and lag probably. So I won't be able to lag-test them ever, probably. Sony PVM (20L5, 14L5, 20M7MDE all take 480p) and GDM (especially the F520) are my highest recommendations for Melee lagless CRT monitors.
