usepackage{algorithm,algpseudocode}
usepackage{etoolbox}
usepackage{tocloft}

patchcmd{listof}% <cmd>
  {float@listhead}% <search>
  {@namedef{l@#1}{l@figure}float@listhead}% <replace>
  {}{}% <success><failure>

pretofigure{%
  ifnumvalue{figure}=0addtocontents{lof}{{bfseries Chapter thechaptervskip10pt}}fi
}
pretotable{%
  ifnumvalue{table}=0addtocontents{lot}{{bfseries Chapter thechaptervskip10pt}}fi
}
pretoalgorithm{%
  ifnumvalue{algorithm}=0addtocontents{loa}{{bfseries Chapter thechaptervskip10pt}}fi
}

cftsetindents{figure}{0em}{3.5em}
cftsetindents{table}{0em}{3.5em}

%% LyX 2.2.1 created this file.  For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
documentclass[12pt,english]{extreport}
usepackage{mathpazo}
usepackage{berasans}
renewcommand{ttdefault}{cmtl}
renewcommand{familydefault}{sfdefault}
usepackage[T1]{fontenc}
usepackage[latin9]{luainputenc}
usepackage[a4paper]{geometry}
geometry{verbose,tmargin=2.5cm,bmargin=2.5cm,lmargin=3cm,rmargin=2cm}
setcounter{secnumdepth}{3}
setcounter{tocdepth}{3}
usepackage{babel}
usepackage{array}
usepackage{longtable}
usepackage{varioref}
usepackage{float}
usepackage{textcomp}
usepackage{multirow}
usepackage{amstext}
usepackage{graphicx}
usepackage{setspace}
onehalfspacing

makeatletter

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
%% Because html converters don't know tabularnewline
providecommand{tabularnewline}{\}
floatstyle{ruled}
newfloat{algorithm}{tbp}{loa}[chapter]
providecommand{algorithmname}{Algorithm}
floatname{algorithm}{protectalgorithmname}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
usepackage{algorithm,algpseudocode}
usepackage{etoolbox}
usepackage{tocloft}


%letl@tablel@figure

patchcmd{listof}% <cmd>
  {float@listhead}% <search>
  {@namedef{l@#1}{l@figure}float@listhead}% <replace>
  {}{}% <success><failure>

pretofigure{%
  ifnumvalue{figure}=0addtocontents{lof}{{bfseries Chapter thechaptervskip10pt}}fi
}
pretotable{%
  ifnumvalue{table}=0addtocontents{lot}{{bfseries Chapter thechaptervskip10pt}}fi
}
pretoalgorithm{%
  ifnumvalue{algorithm}=0addtocontents{loa}{{bfseries Chapter thechaptervskip10pt}}fi
}

cftsetindents{figure}{0em}{3.5em}
cftsetindents{table}{0em}{3.5em}

@ifundefined{showcaptionsetup}{}{%
 PassOptionsToPackage{caption=false}{subfig}}
usepackage{subfig}
AtBeginDocument{
  deflabelitemii{(circ)}
}

makeatother

begin{document}

tableofcontents{}

pagebreak{}

listoffigures{}

pagebreak{}

listof{algorithm}{List of Algorithms}

pagebreak{}

chapter{Background}

begin{figure}[H]
caption{Fig1}
end{figure}


chapter{System Design}

begin{figure}[H]
caption{Fig2}
end{figure}

begin{algorithm}[H]
begin{algorithmic}[1] If{$x < mu$} State{$hat{x} leftarrow 0$} Else{ } State{$hat{x} leftarrow x$} EndIf end{algorithmic}caption{Custom Zero Minus Means Algorithm}
end{algorithm}

end{document}

usepackage[titles]{tocloft}

pretofigure{%
  ifnumvalue{figure}=0addtocontents{lof}{{noindentbfseries Chapter thechaptervskip10pt}}fi
}
pretotable{%
  ifnumvalue{table}=0addtocontents{lot}{{noindentbfseries Chapter thechaptervskip10pt}}fi
}
pretoalgorithm{%
  ifnumvalue{algorithm}=0addtocontents{loa}{{noindentbfseries Chapter thechaptervskip10pt}}fi
}

documentclass[12pt,english]{extreport}
usepackage{mathpazo}
usepackage{berasans}
renewcommand{ttdefault}{cmtl}
renewcommand{familydefault}{sfdefault}
usepackage[T1]{fontenc}
usepackage[latin9]{luainputenc}
usepackage[a4paper]{geometry}
geometry{verbose,tmargin=2.5cm,bmargin=2.5cm,lmargin=3cm,rmargin=2cm}
setcounter{secnumdepth}{3}
setcounter{tocdepth}{3}
usepackage{babel}
usepackage{array}
usepackage{longtable}
usepackage{varioref}
usepackage{float}
usepackage{textcomp}
usepackage{multirow}
usepackage{amstext}
usepackage{graphicx}
usepackage{setspace}
onehalfspacing

makeatletter

%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
% Because html converters don't know tabularnewline
providecommand{tabularnewline}{\}
floatstyle{ruled}
newfloat{algorithm}{tbp}{loa}[chapter]
providecommand{algorithmname}{Algorithm}
floatname{algorithm}{protectalgorithmname}

%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
usepackage{algorithm,algpseudocode}
usepackage{etoolbox}
usepackage{tocbasic}

DeclareTOCStyleEntry[
  indent=0pt,
  numwidth=3.5em,
  onstarthigherlevel=vskip10ptLastTOCLevelWasLower
]{tocline}{figure}
DeclareTOCStyleEntry[
  level=0,
  beforeskip=10pt,
  indent=0pt,
  numwidth=0pt,
  entryformat=textbf,
  linefill=hfill,
  pagenumberformat=@gobble
]{tocline}{chapterinlistof}

patchcmd{listof}% <cmd>
  {float@listhead}% <search>
  {@namedef{l@#1}{l@figure}float@listhead}% <replace>
  {}{}% <success><failure>

pretofigure{%
  ifnumvalue{figure}=0addcontentsline{lof}{chapterinlistof}{Chapter thechapter}fi
}
pretotable{%
  ifnumvalue{table}=0addcontentsline{lot}{chapterinlistof}{Chapter thechapter}fi
}
pretoalgorithm{%
  ifnumvalue{algorithm}=0addcontentsline{loa}{chapterinlistof}{Chapter thechapter}fi
}

@ifundefined{showcaptionsetup}{}{%
 PassOptionsToPackage{caption=false}{subfig}}
usepackage{subfig}
AtBeginDocument{
  deflabelitemii{(circ)}
}
makeatother

begin{document}
tableofcontents
listoffigures
listof{algorithm}{List of Algorithms}
chapter{Background}
begin{figure}[H]
caption{Fig1}
end{figure}
chapter{System Design}
begin{figure}[H]
caption{Fig2}
end{figure}
begin{figure}[H]
caption{Fig3}
end{figure}
begin{algorithm}[H]
begin{algorithmic}[1] If{$x < mu$} State{$hat{x} leftarrow 0$} Else{ } State{$hat{x} leftarrow x$} EndIf end{algorithmic}caption{Custom Zero Minus Means Algorithm}
end{algorithm}
end{document}