If you do not wish to otherwise change your maths symbols, the best solution is to use the mathspec package:
\documentclass{article}
\usepackage{mathspec}
\setallmainfonts(Digits,Latin){Georgia}
\begin{document}
Hello $a+\mathrm{b}=c$
\end{document}
Here, Georgia will be used for the body text and \mathrm, and Georgia Italic will be used for the italic math glyphs.
The unicode-math package (which I kinda wrote) can also do this, but it's somewhat overkill for your purposes and has the additional downside that you need to also load a Unicode mathematics font. Here's an example:
\documentclass{article}
\usepackage{unicode-math}
\setmainfont{Georgia}
\setmathfont{xits-math.otf}
\setmathfont[range=\mathit]{Georgia Italic}
\begin{document}
Hello $a+b=c$
\end{document}
Note that mathspec will not run (yet) on LuaTeX, so if you need a LuaLaTeX solution then you'll need to use unicode-math for now.
The standard font used by TeX is called Computer Modern, but some document classes may use a different font. The default size also depends on document class, but for the standard classes (book, article, report) at least it is 10pt.
LyX does not change this, so Computer Modern is the default here as well. If they are not used, either you're using a document class that specifies a different font, or you've added a font package to the preamble, or you've at some point changed the LyX default settings.
To make Computer Modern (or the new derivative, Latin Modern, which looks similar) the default, go to Document --> Settings --> Fonts, select one of these for the Roman font (and possibly for Sans Serif and Typewriter as well), and click the button labeled Save as document defaults.
Best Answer