You could take a two-stage approach: First, define a new, chapter-like sectioning command that instructs LaTeX to leave greater-than-normal amounts of whitespace above and below the sectioning lines and second, redefine the \listoftables and \listoffigures commands to employ this special sectioning command.
Using the report class as a starting point, you can execute this approach as shown in the MWE below. The new commands are called, somewhat longwindedly, \chapterwithextraspace and \chapterwithextraspace*, to create numbered and unnumbered chapters that have more vertical whitespace than the "standard" commands do. You are of course free to revise the code to select a snappier name. Since you didn't indicate just how much more vertical whitespace you want to create, I've simply doubled the default amounts for this MWE (from 50pt to 100pt above the sectioning line, and from 40pt to 80pt below the sectioning line). You should probably adjust these amounts to suit your specific needs.
\documentclass{report}
\usepackage{etoolbox,lipsum} % lipsum for filler text
% Part 1: Define new command \chapterwithextraspace and
% several required auxilliary macros
\makeatletter
\newcommand\chapterwithextraspace{\if@openright\cleardoublepage\else\clearpage\fi
\thispagestyle{plain}%
\global\@topnum\z@
\@afterindentfalse
\secdef\@chapterwithextraspace\@schapterwithextraspace}
\def\@chapterwithextraspace[#1]#2{\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\protect\numberline{\thechapter}#1}%
\else
\addcontentsline{toc}{chapter}{#1}%
\fi
\chaptermark{#1}%
\addtocontents{lof}{\protect\addvspace{10\p@}}%
\addtocontents{lot}{\protect\addvspace{10\p@}}%
\if@twocolumn
\@topnewpage[\@makechapterwithextraspacehead{#2}]%
\else
\@makechapterwithextraspacehead{#2}%
\@afterheading
\fi}
\def\@makechapterwithextraspacehead#1{%
\vspace*{100\p@}% %default: 50\p@
{\parindent \z@ \raggedright \normalfont
\ifnum \c@secnumdepth >\m@ne
\huge\bfseries \@chapapp\space \thechapter
\par\nobreak
\vskip 20\p@
\fi
\interlinepenalty\@M
\Huge \bfseries #1\par\nobreak
\vskip 80\p@ %default: 40\p@
}}
\def\@schapterwithextraspace#1{\if@twocolumn
\@topnewpage[\@makeschapterwithextraspacehead{#1}]%
\else
\@makeschapterwithextraspacehead{#1}%
\@afterheading
\fi}
\def\@makeschapterwithextraspacehead#1{%
\vspace*{100\p@}% %default: 50\p@
{\parindent \z@ \raggedright
\normalfont
\interlinepenalty\@M
\Huge \bfseries #1\par\nobreak
\vskip 80\p@ %default: 40\p@
}}
\makeatother
% Part 2: Patch the `\listoffigures` and `\listoftables` commands to use the new,
% spaced-out chapter heading style
\patchcmd{\listoffigures}%
{\chapter*}{\chapterwithextraspace*}{}{}
\patchcmd{\listoftables}%
{\chapter*}{\chapterwithextraspace*}{}{}
\begin{document}
\tableofcontents
\listoftables
\listoffigures
\chapter{Hello} %normal chapter header
\lipsum[1]
\chapterwithextraspace{Goodbye} %chapter header with extra space above and below header lines
\lipsum[2]
\end{document}