There's 0 lag on the landing, the whole sequence takes 6 frames (5 jumpsquat, 1 for the DJ).
This technique isn't exactly new, Peach could do it in Melee as could Yoshi, but obv not oos. It's much easier now, though, primarily because you can pseudo-buffer jumps with the Control-Stick (if you have been holding up on the Control-Stick with Tap Jump on for 3 or less frames before you could jump and are still holding up on the frame you can jump, you'll jump on the first possible frame). Due to this Jump->Tap Jump already makes the technique easy. The inputs suggested above, though, also abuse Brawl C-Stick mechanics in a pretty nifty way (you have to press down on the C-Stick within 4 frames after Tap jumping, not on the same frame):
C-Stick down counts as A+Control Stick down for 1 frame. A doesn't do anything in this case (we're in jumpsquat), but as the game sees the Control-Stick as down for 1 frame it treats it as if it had been pushed up again on the next frame, when in reality it's just hold up. Now due to Tap Jump pseudo-buffering you always DJ on the first frame possible as long as the Control-Stick is held up. (Yoshi/Peach jumpsquat is 5 frames, 1 of which is used for the jump input, 1 for the C-Stick input, so Control-Stick is held up at most 3 frames before the DJ can occur)
To get a perfect DJ the timing window for both the C-Stick method and just using Jump->Tap Jump is 4 frames each, but pressing Up for the Tap-Jump one frame late gives you a 1 frame slower DJ that still lands laglessly, while one frame late on the C-Stick results in a DAir (unless you'd hold A during the whole sequence, in that case it'd give you the same result). I find Jump->Tap Jump to be much easier personally, but that's partially just be because I'm doing it all the time for Lucas DJCs anyway.