Without seeing what you're doing, it's hard to tell, but LyX has a way to process files using XeTeX, so this would probably be the simplest route for you to take.
For example, the following document should compile directly using XeLaTeX.
To set LyX to use XeTeX go to Document→Settings→Fonts and choose the option Use non-TeX fonts (via XeTeX/LuaTeX).
The Gentium Plus font can be found here: Gentium Plus. Other fonts on your system may also have the correct characters. With XeTeX, you can use any font that is installed on your system.
Not every font has all the font shapes (e.g. italics) or weights (e.g. bold) that you might need, so you may need to experiment a bit with fonts that have all them. Linux Libertine O seems to, as do Charis SIL (also available from SIL at the link above) and the Brill fonts.
% !TEX TS-program = XeLaTeX