1920 x 1080 works fine, but it can be a little cramped because Lightroom Classic can’t show as many side panels at once, vertically. So you might scroll more often because you can’t see as many folders/collections/options at once. Also, at 1080 pixels tall minus UI, a vertical image is displayed with so few pixels that it’s hard to do any detail work without magnifying. 1920 x 1080 is the minimum size in the Lightroom Classic system requirements.
Higher resolution displays are nice because all of the above problems are reversed: You can see more side panel information at once, and a vertical image at Fit magnification show more detail. But what Cletus said is important, not only because your graphics hardware must be able to draw 4K to 6K worth of pixels fast enough. 4K equals 8.3 megapixels, and 5K equals about 15 megapixels. This is important because of what we’ve observed about Lightroom Classic performance: Performance complaints seem to go up on higher resolution displays, and it’s thought that this is at least partially related to the sheer number of pixels Lightroom Classic has to re-render with every edit. For comparison, my 27" 2560 x 1440 pixel display is just 3.7 megapixels to update, and I often wonder if that’s a major reason Lightroom Classic seems to perform well on my unremarkable Core i5 CPU.
Related: The higher the display resolution, the bigger your 1:1 previews and default Standard previews are going to be, so if you use those preview sizes and the size of your Lightroom Classic previews file already takes up a significant part of the free space on your storage volume, decide how you want to handle that if you increase your display resolution. For example, change default preview sizes or migrate to a bigger volume.
When I create tutorial videos about Lightroom or Photoshop I set my screen to 1920x1080 because that is the size of Full HD video.
That is an example of where 1920 x 1080 is the right thing to do. A big problem with video tutorials is that some people demo with their large displays set to 2560 x 1440 or higher, so when they post their videos, menus and tools are too small to see on smaller displays. When a video tutorial is 1920 x 1080, everything is easy to see on most display sizes…so thanks for doing that!