I finally solved the problem by adapting an answer I saw on Stack Exchange at https://tex.stackexchange.com/questions/730693/place-a-figure-and-table-side -by-side-and-aligned-at-the-top-in-a-figure-float/730738#730738. Here is my code which is placed with a LyX macro box (Ctrl + L):
%% https://tex.stackexchange.com/questions/730693/place-a-figure-and-table-side -by-side-and-%% aligned-at-the-top-in-a-figure-float/730706#730706 \usepackage{graphicx} \usepackage{caption} \usepackage{booktabs} \usepackage{paracol} \globalcounter* \setcolumnwidth{8cm} \begin{paracol}{2} \begin{figure} \includegraphics[width=\linewidth]{Plots/Kurtosis Minimization.png} \caption{Projections onto the kurtosis minimizing vector} \label{fig:KurtosisMinProjections} \end{figure} \switchcolumn \begin{table} \caption{The kurtosis minimizing projection vector} \label{tab:KurtosisMinProjectionVector} \centering \begin{tabular}{lr} \toprule Feature & \hphantom{22222} Projection Vector \\ \midrule \midrule Sepal.Length & 0.988068380 \hphantom{22} \\ \midrule Sepal.Width & 0.114840009 \hphantom{22} \\ \midrule Petal.Length & -0.102380058 \hphantom{22} \\ \midrule Petal.Width & 0.007139457 \hphantom{22} \\ \bottomrule \end{tabular} \end{table} \end{paracol}
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