documentclass{report}
usepackage{etoolbox}  % or xpatch

makeatletter

    % initial definitions of the part info (name and number)
    defthisparttitle{}defthispartnumber{}
    defthischaptertitle{}defthischapternumber{}

    newtoggle{noFigs}
    newtoggle{noTabs}

    apptocmd{@chapter}{gdefthischaptertitle{#1}gdefthischapternumber{thechapter}globaltoggletrue{noFigs}}{}{}
    apptocmd{@part}{gdefthisparttitle{#1}gdefthispartnumber{thepart}globaltoggletrue{noFigs}globaltoggletrue{noTabs}}{}{}

    % the figure environment does the job: the first time it is used after a chapter command, it writes the information of the chapter to the LoF
    AtBeginDocument{%
        AtBeginEnvironment{figure}{%
            iftoggle{noFigs}{
                addtocontents{lof}{protectcontentsline{part}%
                    {protectnumberline{thisparttitle}}{}{3.2em} }
                addtocontents{lof}{protectcontentsline {chapter}%
                    {protectnumberline {thischapternumber} {thischaptertitle}}{}{} }
                globaltogglefalse{noFigs}
            }{}
        }%
        AtBeginEnvironment{table}{%
            iftoggle{noTabs}{
                addtocontents{lot}{protectcontentsline{part}%
                    {protectnumberline{thisparttitle}}{}{} }
                addtocontents{lot}{protectcontentsline {chapter}%
                    {protectnumberline {thischapternumber} {thischaptertitle}}{}{} }
                globaltogglefalse{noTabs}
            }{}
        }%
    }


makeatother

begin{document}

    tableofcontents
    listoffigures


    part{The first}

    chapter{Introduction with no Figures}

    chapter{Test Chapter with Figures}
    begin{figure}
        caption{caption text}
    end{figure}
    begin{figure}
        caption{caption text}
    end{figure}

    chapter{Test Chapter with no Figures}

    part{The second}

    chapter{Another Test Chapter with Figures}
    begin{figure}
        caption{caption text}
    end{figure}
    begin{figure}
        caption{caption text}
    end{figure}
    begin{figure}
        caption{caption text}
    end{figure}
    begin{figure}
        caption{caption text}
    end{figure}
    begin{figure}
        caption{caption text}
    end{figure}

end{document}