tabu package - gaps in vertical lines

One way is to shift up the skip prior to the mid-height \tabucline with a \\[-1pt]. See below for 2nd approach.

%Dokumentclass
\documentclass[landscape]{letter}

%Packages
\usepackage[landscape]{geometry}
\usepackage[utf8]     {inputenc}
\usepackage           {multirow}
\usepackage           {tabu}

%Formatting
\pagestyle{empty} %Remove numbering

\begin{document}
  \begin{tabu}{ |[1pt] l | l l | l | l |[1pt] }
                                                                                                                 \tabucline[1 pt]{1-5}
    \multicolumn{2}{ |[1pt] l }{ } & \multicolumn{3}{ |[1pt] l |[1pt]}{ }                                     \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } & \multicolumn{2}{  l |[1pt] }{ }   \\                       \hline
 y   &                              & \multicolumn{1}{ |[1pt] l |     }{ } & \multicolumn{2}{  l |[1pt] }{ }   \\[-1pt]   \tabucline[1 pt]{3-5} 
\hline
 x   &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\ \tabucline[1 pt]{1-5}
  \end{tabu}
\end{document}

---

Alternately, if you want the thin line to bisect the thick line, then the approach: \\[-1pt] \tabucline[1 pt]{3-5}\\[-12.5pt]\hline works.

%Dokumentclass
\documentclass[landscape]{letter}

%Packages
\usepackage[landscape]{geometry}
\usepackage[utf8]     {inputenc}
\usepackage           {multirow}
\usepackage           {tabu}

%Formatting
\pagestyle{empty} %Remove numbering

\begin{document}
  \begin{tabu}{ |[1pt] l | l l | l | l |[1pt] }
                                                                                                                 \tabucline[1 pt]{1-5}
    \multicolumn{2}{ |[1pt] l }{ } & \multicolumn{3}{ |[1pt] l |[1pt]}{ }                                     \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } & \multicolumn{2}{  l |[1pt] }{ }   \\                       \hline
 y   &                              & \multicolumn{1}{ |[1pt] l |     }{ } & \multicolumn{2}{  l |[1pt] }{ }   \\[-1pt]   \tabucline[1 pt]{3-5}\\[-12.5pt]
\hline
 x   &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\                       \hline
    &                              & \multicolumn{1}{ |[1pt] l |     }{ } &                                 & \\ \tabucline[1 pt]{1-5}
  \end{tabu}
\end{document}