I have used Lilypondtool both on Windoze, and on Ubuntu, and the toolbar immediately above the open file has little icons for everything you need. One of them is a tiny sheet of paper representing the PDF option. Do you have that on your version? If so, simply click that (once not twice) and your PDF should appear in a separate window in jEdit's native PDF viewer. Especially if your compilation creates a ./ file name as I see it does.