Still an issue on this website getting from email notifications into the topic on the Forum because the hyperlink function in the emails is still broken and the webmaster, after being advised some time ago, has still failed to either acknowledge it or fix it. Anyhow, by copy/paste I'm here, so let's deal with the topic.
I am using Lightroom Classic on OSX, latest version. There are two modes for the tone curve: (a) adjusting the curve on the curve where no parametric controls show, or (b) parametric using the four sliders provided under the tone curve interface. If you are using method (a), the only way to adjust the curve is by moving points on the curve directly with your mouse, trackpad, etc.. If you are using method (b), you can either slide the parametric sliders, or you can dial numeric values into the number boxes to the right of the sliders. In neither case do arrow keys work.
There is a general under-use of arrow keys in the Lightroom application. It would enhance user control over fine adjustment to be able to move curve points with the arrow keys. Likewise, in the Print Module, for positioning prints in Custom layout mode, I have long ago recommended to Adobe that they enable the arrow keys to nudge prints into position. Heck, I can do this with a cheap application called "Snagit" (for screen grabs and their editing), why can't a sophisticated operation like Adobe provide this functionality in Lightroom?
Anyhow, those are the ways to use LR's tone curve. These are quibbles - it's a good tool, does the needful, just a matter of becoming nimble in adjusting it.