With the KOMA-Script class scrbook the default line filling for section (and subsection etc.) entries in TOC is \TOCLineLeaderFill. The distance between the dots depends on the size of the dots and the font. So you have to use
\newcommand\Dotfill{{\normalfont\normalsize \TOCLineLeaderFill}}
Then the dots between the chapter title and the date are aligned with the dots after the section title.
But it is difficult to align the dots between the date and the page number with the dots of the section entries. Here is a suggestion that still needs adjustment depending on the font size and \@dotfil.
\documentclass[headings=optiontotocandhead]{scrbook}
\usepackage{lipsum}% only for dummy text
\DeclareTOCStyleEntry[
linefill={},
]{tocline}{chapter}
\newcommand\Dotfill{{\normalfont\normalsize \TOCLineLeaderFill}}
\newlength{\leaderboxwidth}
\setlength{\leaderboxwidth}{43.8pt}% <- adjust here
\DeclareRobustCommand*{\toclineinsert}[1]{%
{\normalfont\Dotfill {#1}\makebox[\leaderboxwidth][l]{\Dotfill}}%
}
\begin{document}
\frontmatter
\tableofcontents
\mainmatter
\addchap
[tocentry={First lecture title \toclineinsert{4 January}},head={}]
{Second lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={Second lecture title \toclineinsert{2nd half January}},head={}]
{Second lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={Third lecture title \toclineinsert{Arpil/March}},head={}]
{Third lecture title}
\addsec[tocentry={Questions and answers},head={}]{}
\end{document}
\documentclass[headings=optiontotocandhead]{scrbook}
\usepackage{lipsum}% only for dummy text
\DeclareTOCStyleEntry[
linefill=\TOCLineLeaderFill,
raggedentrytext=true
]{tocline}{chapter}
\DeclareRobustCommand*{\toclineinsert}[1]{{\ \normalfont\mbox{(#1)}}}
\begin{document}
\tableofcontents
\addchap
[tocentry={first lecture title \toclineinsert{4 January}}]
{first lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={second lecture title \toclineinsert{2nd half January}},head={different entry in page header}]
{second lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={third lecture title \toclineinsert{February/March}}]
{third lecture title}
\addsec[tocentry={Questions and answers},head={}]{}
\end{document}

But I would suggest to use either
\documentclass[headings=optiontotocandhead]{scrbook}
\usepackage{lipsum}% only for dummy text
\DeclareTOCStyleEntry[
linefill=\TOCLineLeaderFill,
raggedentrytext=true
]{tocline}{chapter}
\DeclareRobustCommand*{\toclineinsert}[1]{{\normalfont\mbox{(#1)}}}
\begin{document}
\tableofcontents
\addchap
[tocentry={first lecture title \toclineinsert{4 January}}]
{first lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={second lecture title \toclineinsert{2nd half January}},head={different entry in page header}]
{second lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={third lecture title \toclineinsert{February/March}}]
{third lecture title}
\addsec[tocentry={Questions and answers},head={}]{}
\end{document}

or
\documentclass[headings=optiontotocandhead]{scrbook}
\usepackage{lipsum}% only for dummy text
\DeclareTOCStyleEntry[
linefill={},
]{tocline}{chapter}
\newcommand \Dotfill {{\normalfont\normalsize \TOCLineLeaderFill}}
\DeclareRobustCommand*{\toclineinsert}[1]{%
{\normalfont\Dotfill\mbox{#1\quad}}%
}
\begin{document}
\tableofcontents
\addchap
[tocentry={first lecture title \toclineinsert{4 January}}]
{first lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={second lecture title \toclineinsert{2nd half January}},head={different entry in page header}]
{second lecture title}
\lipsum[1-20]
\addsec[tocentry={Questions and answers},head={}]{}
\addchap
[tocentry={third lecture title \toclineinsert{February/March}}]
{third lecture title}
\addsec[tocentry={Questions and answers},head={}]{}
\end{document}

\leaders? – Parvana Nov 15 '21 at 18:57