LyX ⇒ Lots of symbols don't work

[KMWallace]

I have a lot of trouble using symbols in LyX. On the insert symbol menu, many of the symbols show up only as blank boxes. Sometimes I can get around this by entering the symbol codes in Latex mode, but other times I get an error message like "Could not find LaTeX command for character..." My document encoding is already utf8 and I have Doulos SIL (unicode font) installed on my computer. Can anyone help me solve this problem please?