On a U.S. English keyboard, I don’t think any of those keyboard shortcuts work in Lightroom for moving among images. Are you using another language?
The rest of this post is for U.S. English in case it’s different in other languages:
The keys that do work for previous/next image are the left arrow/right arrow keys, not the < > keys. In the Grid, the up arrow/down arrow keys work too.
What can also work are:
Command-left arrow/Command-right arrow keys (macOS)
Ctrl-left arrow/Ctrl-right arrow keys (Windows)
Those shortcuts also work with Lightroom Classic, especially when the arrow keys aren’t moving among images because the text cursor is moving in a text/number edit field.
For navigation, the Fn key doesn’t help you move to another image. On a compact keyboard, the Fn key does work for scrolling one image in Detail view (Lightroom) or Loupe view (Lightroom Classic), or Photoshop:
Fn + Up Arrow = Page Up (add Shift for scroll left)
Fn + Down Arrow = Page Down (add Shift for scroll right)
Fn + Left Arrow = Home (top left corner)
Fn + Right Arrow = End (bottom left corner)