Simply use \cline{fromcolumn-tocolumn}
.
\documentclass[12pt,a4paper,oneside]{report}
\usepackage{ragged2e}
\usepackage{longtable, makecell}
\newcolumntype{L}[1]{>{\RaggedRight}p{#1}}
\renewcommand\theadfont{\small\bfseries}
\setcellgapes{3pt}
\begin{document}
{\makegapedcells
\begin{longtable}{|c|L{2.5cm}|L{5cm}|L{1.8cm}|L{2.1cm}|}
\caption{My Table}\\
\hline
\thead{No} & \thead{A} & \thead{B} & \thead{C} & \thead{D} \\\hline
%
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
\end{longtable}
}
\end{document}

Edit: in case of a table which goes on many pages, with \pagebreak
you can force a page break to avoid the separation of a group of cells.
\documentclass[12pt,a4paper,oneside]{report}
\usepackage{ragged2e}
\usepackage{longtable, makecell}
\newcolumntype{L}[1]{>{\RaggedRight}p{#1}}
\renewcommand\theadfont{\small\bfseries}
\setcellgapes{3pt}
\begin{document}
{\makegapedcells
\begin{longtable}{|c|L{2.5cm}|L{5cm}|L{1.8cm}|L{2.1cm}|}
\caption{My Table}\\
\hline
\thead{No} & \thead{A} & \thead{B} & \thead{C} & \thead{D} \\\hline
\endfirsthead
\hline
\thead{No} & \thead{A} & \thead{B} & \thead{C} & \thead{D} \\\hline
\endhead
%
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
\pagebreak
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
1 & FOO-01 & Lorem ipsum dolor sit amet & John & Lorem \\\cline{1-3}
1.1 & FOO-01-01 & consectetur adipiscing elit. & & \\\cline{1-3}
1.2 & FOO-01-02 & curabitur ut quam eu. & & \\\hline
2 & FOO-02 & Nam posuere turpis et & Doe & Ipsum\\\cline{1-3}
2.1 & FOO-02-01 & consectetur adipiscing elit. & &\\\cline{1-3}
2.2 & FOO-02-02 & curabitur ut quam eu. & &\\\hline
\end{longtable}
}
\end{document}

