Redefine \chapterformat in the same way:
\renewcommand*{\chapterformat}{%
\makebox[\mysecnumhang][l]{\thechapter\autodot\enskip}%
}
and redefine \chapterlinesformat:
\renewcommand{\chapterlinesformat}[3]{%
\sbox\tmpseclinenobox{#2}%
\ifdim\wd\tmpseclinenobox>0pt\hspace{-\mysecnumhang}\fi
\expandafter\headuline{#2#3}%
}
or
\renewcommand{\chapterlinesformat}[3]{%
\Ifstr{#2}{}{}{\hspace{-\mysecnumhang}}%
\expandafter\headuline{#2#3}%
}
Example:
\PassOptionsToPackage{svgnames,table,dvipsnames}{xcolor}
\documentclass[a4paper,10pt,oneside,DIV=9]{scrbook}
% demo only
\usepackage{mwe}
% Packages
\usepackage{scrlayer-scrpage}
\usepackage{xcolor} % showframe loads this
\usepackage[normalem]{ulem}
\usepackage{hyperref}
% theme colours
\definecolor{MyThemeColour}{cmyk}{0.10,0.10,1.00,0} % personal yellow
\newlength{\mysecnumhang}
\setlength{\mysecnumhang}{30pt}
% KOMA and general setup
\renewcommand{\chapterformat}{%
\makebox[\mysecnumhang][l]{\thechapter\autodot\enskip}%
}
\renewcommand{\sectionformat}{%
\makebox[\mysecnumhang][l]{\thesection\autodot\enskip}%
}
\renewcommand{\subsectionformat}{%
\makebox[\mysecnumhang][l]{\thesubsection\autodot\enskip}%
}
\renewcommand{\subsubsectionformat}{%
\makebox[\mysecnumhang][l]{\thesubsubsection\autodot\enskip}%
}
\renewcommand{\chapterlinesformat}[3]{%
\Ifstr{#2}{}{}{\hspace{-\mysecnumhang}}%
\expandafter\headuline{#2#3}%
}
\renewcommand{\sectionlinesformat}[4]{%
\Ifstr{#3}{}{}{\hspace{-\mysecnumhang}}%
\expandafter\headuline{#3#4}%
}
\newcommand\headuline{%
\bgroup\markoverwith{\textcolor{MyThemeColour}{\rule[-0.75ex]{1pt}{1pt}}}\ULon% 2pt 2pt
}
% recalc the text block after all the font loading
\KOMAoptions{DIV=last}
\begin{document}
\addchap{Foo}
\addsec*{Lipsum}
Some text.
\section{Lipsum}
\blinddocument
\end{document}
Additional remark: The solution is limited to one line headings because of the underline.
Regarding a comment below:
If you visualize the bounding box of the letters in the headings (using eg. https://tex.stackexchange.com/a/57860), the alignment of the heading texts will be visible:

Code for the picture:
\PassOptionsToPackage{svgnames,table,dvipsnames}{xcolor}
\documentclass[a4paper,10pt,oneside,DIV=9]{scrbook}
% demo only
\usepackage{mwe}
% Packages
\usepackage{scrlayer-scrpage}
\usepackage{xcolor} % showframe loads this
\usepackage[normalem]{ulem}
%\usepackage{hyperref}
% theme colours
\definecolor{MyThemeColour}{cmyk}{0.10,0.10,1.00,0} % personal yellow
\newlength{\mysecnumhang}
\setlength{\mysecnumhang}{30pt}
% KOMA and general setup
\renewcommand{\chapterformat}{%
\makebox[\mysecnumhang][l]{\thechapter\autodot\enskip}%
}
\renewcommand{\sectionformat}{%
\makebox[\mysecnumhang][l]{\thesection\autodot\enskip}%
}
\renewcommand{\subsectionformat}{%
\makebox[\mysecnumhang][l]{\thesubsection\autodot\enskip}%
}
\renewcommand{\subsubsectionformat}{%
\makebox[\mysecnumhang][l]{\thesubsubsection\autodot\enskip}%
}
\renewcommand{\chapterlinesformat}[3]{%
\Ifstr{#2}{}{}{\hspace{-\mysecnumhang}}%
\expandafter\headuline{#2#3}%
}
\renewcommand{\sectionlinesformat}[4]{%
\Ifstr{#3}{}{}{\hspace{-\mysecnumhang}}%
\expandafter\headuline{#3#4}%
}
\newcommand\headuline{%
\bgroup\markoverwith{\textcolor{MyThemeColour}{\rule[-0.75ex]{1pt}{1pt}}}\ULon% 2pt 2pt
}
% recalc the text block after all the font loading
\KOMAoptions{DIV=last}
% show bounding box for each letter (https://tex.stackexchange.com/a/57860)
\makeatletter
\def\showboxes#1{%
\begingroup\color{red}\fboxrule=.1pt \fboxsep=-\fboxrule
@showboxes#1@showboxes@empty
\endgroup}
\def@showboxes#1#2{%
\ifx#2@showboxes
\fbox{\color{gray}#1}\expandafter@gobble
\else
\setbox0=\hbox{#1\kern0pt#2}\setbox2=\hbox{#1#2}%
\dimen0=\wd0 \advance\dimen0 -\wd2 % \dimen0 contains the kern between the two chars
\fbox{\color{gray}#1}\kern-\dimen0
\expandafter@showboxes
\fi#2}
\begin{document}
\chapter{\showboxes{Lipsum}}
\section{\showboxes{Lipsum}}
\end{document}