I have experienced this problem as well.
This is what I am doing when I experience the problem on the website. I add a new song, copy lyrics into the shared lyrics section, and save the file. In the Song Edit mode, "Lyrics" appears under the document heading. When on the Songs page, If you hover over the "document" icon when viewing your song nothing appears. If you click on the icon, nothing comes up. When I use the app on my android device or iPad and click on the "document" icon, the lyrics appear just fine.