Use the tocloft package which enables control of many aspects of the ToC and friends.
% frontispieceprob.tex SE 576148
\documentclass{book}
\usepackage{graphicx}
\usepackage{tocloft}
\begin{document}
THE FRONTISPIECE
\vspace{4\baselineskip}
% The frontispiece picture and caption
\includegraphics[width=\textwidth]{image.jpg}
\begin{center}
Image caption
\end{center}
% add it to the LoF
\cftlocalchange{lof}{3em}{2.55em} % need more space for page designation
\cftaddtitleline{lof}{figure}{Image caption}{frontis} % the LoF entry
\cftlocalchange{lof}{1.55em}{2.55em} % revert to normal page number space
\clearpage
\tableofcontents
\listoffigures
\chapter{A Chapter}
\begin{figure}
\centering
AN ILLUSTRATION
\caption{An illustration}
\end{figure}
\end{document}
If you don't increase the allowable space for page numbers then the dotted line continues into "frontis".
I've just done a crude frontispiece page; I'm sure yours is much better.

titlepageor what? – egreg Dec 23 '20 at 13:07includegraphicscommand on an empty page in thearticleclass. So I guess my question might boil down to whether I can replace the page number with arbitrary text when adding a manual entry to the lof. – Ubiquitous Dec 23 '20 at 13:14\addtocontents{lof}{\protect\contentsline{figure}{caption}{frontis}}would work (cf. https://tex.stackexchange.com/questions/203158/how-to-add-custom-lines-with-specified-page-number-to-the-table-of-contents). – Marijn Dec 23 '20 at 15:31