Is this textbook written in LaTeX?

This seems to be done by Acrobat Distiller. In every case, you may send a polite mail to the publisher and will get the info for sure. Your question on how to reproduce this is too broad for this site.

this book was written with latex or lyx:

1- the question and answer was written with tcolorbox and multicolumn:

\usepackage{tikz,lipsum}
\tcbuselibrary{skins,breakable}
\newcounter{example}
\colorlet{colexam}{green!45!black}
\newtcolorbox[use counter=example]{myexample}{%
70
empty,title={\colorbox{green!45!black}{\textcolor{white}{Example \thetcbcounter}\textcolor{green!45!black}{\thinspace text text text}},attach boxed title to top left,
boxed title style={empty,size=minimal,toprule=2pt,top=4pt,
overlay={\draw[colexam,line width=2pt]
([yshift=-1pt]frame.north west)--([yshift=-1pt]frame.north east);}},
coltitle=colexam,fonttitle=\Large\bfseries,
before=\par\medskip\noindent,parbox=false,boxsep=0pt,left=0pt,right=3mm,top=4pt,
breakable,pad at break*=0mm,vfill before first,
overlay unbroken={\draw[colexam,line width=1pt]
([yshift=-1pt]title.north east)--([xshift=-0.5pt,yshift=-1pt]title.north-|frame.east)
--([xshift=-0.5pt]frame.south east)--(frame.south west); },
overlay first={\draw[colexam,line width=1pt]
([yshift=-1pt]title.north east)--([xshift=-0.5pt,yshift=-1pt]title.north-|frame.east)
--([xshift=-0.5pt]frame.south east); },
overlay middle={\draw[colexam,line width=1pt] ([xshift=-0.5pt]frame.north east)
--([xshift=-0.5pt]frame.south east); },
overlay last={\draw[colexam,line width=1pt] ([xshift=-0.5pt]frame.north east)
--([xshift=-0.5pt]frame.south east)--(frame.south west);},%
}
\begin{myexample}
\lipsum[1]
\end{myexample}

2- the bold and red Caption:

    \usepackage[labelformat=simple,labelsep=colon,textformat=simple,justification=justified,font=scriptsize]{caption}
\usepackage{color}
\captionsetup{labelfont={color=red,bf},
textfont={color=black}}