Whole page table with tabularx

you have some issues, first off the 290mm should really be \linewidth or \textwidth. Second, you should put a \noindent in front of the tabular. And finally, not so much of an issue, remove the page number.

\documentclass[a4paper,12pt]{scrartcl}
\usepackage{pdflscape}
\usepackage{tabularx}
\usepackage{lipsum}

\begin{document}
  \begin{landscape}
    \thispagestyle{empty}
    \noindent
    \begin{tabularx}{\linewidth}{|c|c|c|X|}
      \hline
      Lorem & Lorem & Lorem & \lipsum[1] \\
      \hline
    \end{tabularx}
  \end{landscape}
\end{document}

To address the comment, it's not how I read it, but if that is in fact the case, the following can be used (Adjusted after egreg's comment):

\centering\makebox[0pt][c]{%
  \hskip-\footskip
  \begin{tabularx}{\paperheight}{|c|c|c|X|}
    \hline
    Lorem & Lorem & Lorem & \lipsum[1] \\
    \hline
  \end{tabularx}%
  \hskip\headheight
}

You have a paragraph indent to the left of the table and the specified width is considerably more than the horizontal size, because of the margins. try

  \noindent\begin{tabularx}{\hsize}{|c|c|c|X|}