The website notes that you can measure lag with an “expensive” high-speed camera setup.
My favorite trick, which I’ve used frequently (including in scientific publications on lag!) is to use the slo-mo cam on a smartphone. Phones will usually do anywhere from 120-240Hz. Set up the camera so it can see both your input (e.g. a side view of you pushing a button) and the display, record a video, and then pull it into a media player that supports frame-by-frame playback. You can then measure the number of frames elapsed from you pushing the button (pressing it down far enough to electrically activate it) and the corresponding reaction on screen. This gives you a cheap and easy setup capable of measuring latency down to ~4ms granularity, and doing a few repeated measurements can give you a very accurate picture of latency. Keep in mind that latency is a range (statistical distribution), not a single number, so you need repeated measurements to understand the shape of the distribution.
If you’re developing a game, you can add a prominent frame counter on screen to be captured on the video, and add the frame counter to your log output. Then you can match up the video with your game’s events, after accounting for display latency.
I don't know how scientifically valid this is (I hope very) but when a friend told me my USB hub / switcher would be introducing a lot of input lag, I bought a USB to eth adaptor and did a few thousand pings to the router, from direct to mobo and then from via the switcher. Unsurprisingly, there was no measurable latency (I had to use a 3P tool because Windows wouldn't go lower than ms by default).
I am aware that admitting to using Windows in these hallowed halls is a terrible sin, but the anecdote was too relevant to pass up and that's an important detail for anybody looking to repro.