embark-prefix-help-command fails to show key bindings under lsp-mode

[richcarl]

When using (setq prefix-help-command #'embark-prefix-help-command), normally everything is fine, but for some reason in combination with lsp-mode (which uses a right-click popup menu), it doesn't show you the actual key bindings, but only "menu-item" (even though these items do have keybindings as well as being in the menu):

Whereas if you use the standard prefix-help-command, it succeeds in showing you the bindings:

I can't tell if it's embark-bindings-in-keymap that needs to be more clever, or if it's lsp-mode's lsp-define-conditional-key that does something in a nonstandard way.