
LyX and MikTeX

Code:
\documentclass[12pt]{article}
\usepackage{amssymb} %this is for \mathbb code
\begin{document}
$\Gamma(s)=\displaystyle\int \limits_0^{\infty} e^{t} t^{s1} ~ dt$ for $s\in\mathbb{R}$.
\end{document}
works with me in WinEdt 5.5.

LyX help
the LateX button is for inserting raw code, in LateX you need to use the dollar signs to designate a formula.
LyX has a special keyboard shortcut for math formulas, just type command(control)shiftM and that will insert a floating formula where you can intuitively enter formulas.
more math options can be found if you go to the 'insert' menu and select the 'math' submenu.
hope that helped!