The following example shows a possible solution, but I have no idea how to implement it in LyX. You can use two side by side minipages; the first one will contain the text, and the second one will contain the image. A little example:
\documentclass{report}
\usepackage[demo]{graphicx}
\begin{document}
\noindent\begin{minipage}{.55\textwidth}
\bfseries
\Huge Some Text \\
Some Text \\
\Large Some more text \\
Some more text \\
\normalsize And even more text \\
And even more text
\end{minipage}%
\begin{minipage}{.45\textwidth}
\centering
\includegraphics[height=3cm]{name}
\end{minipage}
\end{document}
Feel free to adjust the width of the minipages and the image height according to your needs. I used the demo option for the graphicx package to make my example compilable for everyone; do not use that option in your actual code.
