If you really need Verdana, you must use XeTeX. This is not officially supported (yet) but there are workarounds. Search for XeTeX at the wiki (http://wiki.lyx.org).
On 2009-06-13, Richard Talley wrote: > It can be hard to find typefaces that look excellent on paper and on > screen (and on both Windows and OS X). Sometimes I'll reset a document > in a different typeface when I print it out. The technical documents > I'm producing right now I'm putting in Bera (based on Vera Bitstream, > realist family) as a reasonable compromise. Bitstream Vera (or the extended version DejaVy) is the font used by OpenOffice: like Verdana it is designed for good appearance in both on-screen and printed documents. It is supported in LaTeX by the two packages 'bera' (Vera serif) and 'arev' (sans serif with math support). Günter