The problem is beamer, not LyX, put \usefonttheme{professionalfonts} in your document preamble. I'm using LyX 2.2.2 and it works.
I have found the solution here.
Moreover in your formula you have a \mathbf within another \mathbf.
EDIT:
Thinking of Ulrike Fischer's comment, if you use \mathbf to make everything bold, also the exponent -1 is bold.
It's better to put it only before the matrix and vector symbols (in LyX you may use the math bold option selecting only the variable you want in blod, not the whole formula).
In order to avoid repeating \mathbf everywhere, you may create specific new commands (in LyX you may put the \newcommand declarations in your document preamble and use the new commands directly in math mode).
\documentclass[11pt,twoside,british,openright]{beamer}
\usefonttheme{professionalfonts}
\usepackage{babel}
\newcommand{\matrx}{\mathbf{X}} % Matrix X bold
\newcommand{\matromega}{\mathbf{\Omega}} % Matrix Omega bold
\newcommand{\vecy}{\mathbf{y}} % Vector y bold
\begin{document}
This is the result with \verb|\mathbf| for the whole formula:
\[
=\mathbf{\left(X'\Omega^{-1}X\right)^{-1}\left(X'\,\Omega^{-1}y\right)}
\]
but maybe you prefer this:
\[
=\left(\mathbf{X}'\mathbf{\Omega}^{-1}\mathbf{X}\right)^{-1}\left(\mathbf{X}'\,\mathbf{\Omega}^{-1}\mathbf{y}\right)
\]
obviously using some new commands to avoid repeating \verb|\mathbf| everywhere, the result is the same:
\[
=\left(\matrx'\matromega^{-1}\matrx\right)^{-1}\left(\matrx'\,\matromega^{-1}\vecy\right)
\]
\end{document}
