In the event that the CPU is faster than the GPU, the CPU run ahead of the GPU and queue multiple frames to render, regardless of adaptive sync or not. This adds lag. Adaptive sync or high Hz only gets rid of up to one frame of delay from vsync timing, not delay from excess frame queuing.

What Anti-Lag does is throttle the CPU work to reduce this delay to as low as sub-frame, so it doesn't process input and begin frame processing until closer to display time -- so the game starts frame updates with fresher input and gets those frames out with less delay. Graphics APIs often only allow setting the frame queue length in an integer number of frames and it can be difficult to reliably tell when frames present and control frame queuing, especially with a compositor involved. This has the graphics driver involved, so it knows the absolute truth of when frames hit the output.

Presumably it doesn't require an expensive monitor.

If you don't underestimate the render time (and miss the refresh) then the frame will be fresher.