You could patch \addparttocentry to get an entry for each part in LOF and LOT:
\documentclass{scrbook}
\unsettoc{lof}{chapteratlist}% remove the chapter gap in LOF
\unsettoc{lot}{chapteratlist}% % remove the chapter gap in LOT
\usepackage{xpatch}
\xapptocmd\addparttocentry{%
\addxcontentsline{lof}{part}[{#1}]{#2}% copy the part entry to LOF
\addxcontentsline{lot}{part}[{#1}]{#2}% copy the part entry to LOT
}{}{\PatchFailed}
\begin{document}
\listoffigures
\part{Part One}
\chapter{Chapter One}
\captionof{figure}{My first figure}
\captionof{figure}{My second figure}
\chapter{Chapter Two}
\captionof{figure}{A figure in Chapter Two}
\part{Part Two}
\chapter{Chapter Three}
\captionof{figure}{My next figure}
\chapter{Chapter Four}
\addpart{Unnumbered Part}
\chapter{Chapter Five}
\captionof{figure}{My last figure}
\end{document}
Or in all lists controlled by package tocbasic:
\documentclass[listof=ignorechapter]{scrbook}
\usepackage{xpatch}
\makeatletter
\xapptocmd\addparttocentry{%
\doforeachtocfile{%
\ifstr{\@currext}{toc}{}{%
\addxcontentsline{\@currext}{part}[{#1}]{#2}%
}%
}%
}{}{\PatchFailed}
\makeatother
\begin{document}
\listoffigures
\part{Part One}
\chapter{Chapter One}
\captionof{figure}{My first figure}
\captionof{figure}{My second figure}
\chapter{Chapter Two}
\captionof{figure}{A figure in Chapter Two}
\part{Part Two}
\chapter{Chapter Three}
\captionof{figure}{My next figure}
\chapter{Chapter Four}
\addpart{Unnumbered Part}
\chapter{Chapter Five}
\captionof{figure}{My last figure}
\end{document}
Result:

It is also possible to declare a new style for the part entries in the lists. Example without page numbers for the part entries:
\documentclass[listof=ignorechapter]{scrbook}
\usepackage{xpatch}
\makeatletter
\xapptocmd\addparttocentry{%
\doforeachtocfile{%
\ifstr{\@currext}{toc}{}{%
\addxcontentsline{\@currext}{partatlists}[{#1}]{#2}%
}%
}%
}{}{\PatchFailed}
\DeclareTOCStyleEntry[
pagenumberbox=\@gobble,
level=-1,
indent=0pt,
numwidth=0pt,
dynnumwidth
]{part}{partatlists}
\makeatother
\begin{document}
\listoffigures
\part{Part One}
\chapter{Chapter One}
\captionof{figure}{My first figure}
\captionof{figure}{My second figure}
\chapter{Chapter Two}
\captionof{figure}{A figure in Chapter Two}
\part{Part Two}
\chapter{Chapter Three}
\captionof{figure}{My next figure}
\chapter{Chapter Four}
\addpart{Unnumbered Part}
\chapter{Chapter Five}
\captionof{figure}{My last figure}
\end{document}

3,9and15)? How to not include part titles if there is no figure within this part? (I do understand this might be a bit complex, since thelistof=chapterentryoption does not implement it -- i.e. all chapters, even empty, are listed) – ebosi Jan 20 '17 at 09:53