How to align horizontally two tabular environments

I suggest you get rid of the \parbox wrappers. If you want to roughly center the two tabular environments within the width of the text block, consider using a few (more) \hfill instructions.

\documentclass{article}
\usepackage{float,caption}
\begin{document}
\begin{table}[H]
    \caption{Neque porro quisquam est qui dolorem ipsum quia dolor sit amet.}
    \label{table:lorem_ipsum}
    \hfill
        \begin{tabular}[t]{ c | c }
            Lorem & Ipsum \\ 
            \hline
            A   & B \\
            C & D \\
            E & F \\
            G & H \\
            I & J \\
        \end{tabular}
    \hfill
        \begin{tabular}[t]{ c | c }
            Lorem & Ipsum \\ 
            \hline
            K & L \\
            M & N \\
            O & P \\
        \end{tabular}
    \hfill\null
\end{table}
\end{document}

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Addendum: If you must keep the \parbox wrappers, I would suggest you add the [t] positioning specifier in both instances: \parbox[t]{.35\linewidth}{...} and \parbox[t]{.50\linewidth}{...}.

At least for this example, a simple solution (less code) is constructing only one tabular environment with an empty column.

\documentclass{article}
\usepackage{booktabs,caption}
\begin{document}
\begin{table}
\caption{Neque porro quisquam est qui 
         dolorem ipsum quia dolor sit amet.}
\centering
 \begin{tabular}[t]{c|cp{1cm}c|c}
   Lorem & Ipsum && Lorem & Ipsum\\[2pt]           
   \cmidrule{1-2}\cmidrule{4-5}
   A & B && K & L \\
   C & D && M & N \\
   E & F && O & P\\
   G & H && \multicolumn{1}{c}{}\\
   I & J && \multicolumn{1}{c}{}\\
 \end{tabular}
\end{table}
\end{document}