When V-sync is off, the screen is drawn immediately whenever it's ready. This can be half-way through the monitor scan, which means you get tearing, but the display is always updated immediately (ie. no lag).
When V-sync is on, the screen waits until the monitor scan is finished before drawing. This prevents tearing, but fundamentally requires it wait until the monitor is ready, which is the lag you see. I can't remember how Classic works exactly, but there might be one or two other things at work (some kind of buffering) which introduce one or two frame lags as well, which is more noticable in V-sync mode.
So unfortunately you can't have the best of both worlds - either you introduce a delay to fix tearing, or you have tearing.