Can't open example files in LyX (greyed out)
If LyX utilizes the Open File dialog appropriately, you should be able to visit any path directly via the Finder shortcut ⇧⌘G.  Tab completion works in the resulting path dialog.  

If LyX does not allow browsing via path, I would just copy the files to a temporary directory to bypass the difficulty. 

Sidebar
Mac OS is full of very handy keyboard shortcuts that work fairly consistently.  See this link for a fairly comprehensive list. Since you're familiar with UNIX, it may help to note basic Emacs navigation also works in most text editing contexts--C-b, C-f,C-a,C-e, C-k, C-y.