On hindsight, I guess even with lag, I did get some postable races. Enough to make four videos this time. The lag that gets me is when I'm trying to do tricks. Sometimes the trick button on the Pro Controller doesn't trigger when it's supposed to compared to the GamePad (which only acts up once in awhile). I'll post them soon.
When you say it's that kind of lag, then my incredulousness fades (I thought you meant lag like on the analog sticks). That behavior sounds exactly like what I experienced at the Play Nintendo competition in July, where in the final match I could barely drift or use items because the Z buttons weren't responding most of the time. I attributed it to it being a crappy controller that was just used too much in giant events.
That said, I've never had that problem at home. I'd say you should just take yours back and get a different one, but that would require a trip to Japan, wouldn't it. Have you tried re-syncing, just out of superstition? It's also odd still that you say it happens when you're online but not playing just locally.