No idea why 60 Hz on an LCD works better, though.

Because LCD pixels are constantly lit up. They don’t start to dim in between refresh cycles. They may take some time to change from one state to another, but that is perceived as ghosting, not flickering.

On a CRT the phosporus dots are periodically lit up (or “refreshed”) by an electron beam, and then start to dim aftewards. So the lower the refresh rate, the more time they have to dim in between strobes. On low refresh rates this is perceived as flickering. On higher refresh rates, the dots don’t have enough time to noticably dim, so this is perceived as a more stable image. 60Hz happens to the refresh rate where this flicker effect becomes quite noticable to the human eye.