If the changes of the numwidth boxes in the ToC, LoF and LoT should be restricted to some part of the document, the \addtolength{cftchapnumwidth}{10pt} etc. has to be written literally into the relevant ToC - file.
Please note that this might produce inconsistent layout in the ToCs.
The value of 40pt is of course too large, I have used it just for demonstration.
\documentclass[11pt,a4paper]{book}
\usepackage[toc,page]{appendix}
\usepackage{tocloft}
\usepackage{pgffor}
\begin{document}
\tableofcontents
\listoftables
\listoffigures
\clearpage
%
\chapter{Regular content}
\foreach \x in {1,...,10} {%
\begin{figure}
\caption{Figure caption \x}
\end{figure}
\begin{table}
\caption{Table caption \x}
\end{table}
}
\clearpage
\appendix
\addtocontents{toc}{\protect\addtolength{\protect\cftchapnumwidth}{10pt}}
\addtocontents{lof}{\protect\addtolength{\protect\cftfignumwidth}{40pt}}
\addtocontents{lot}{\protect\addtolength{\protect\cfttabnumwidth}{40pt}}
\renewcommand{\thechapter}{A.\Roman{chapter}}
\renewcommand{\thefigure}{\thechapter.\arabic{figure}}
\renewcommand{\thetable}{\thechapter.\arabic{figure}}
%\input{anexo}
\chapter{Appendix content One}
\foreach \x in {1,...,10} {%
\begin{figure}
\caption{Figure caption \x}
\end{figure}
\begin{table}
\caption{Table caption \x}
\end{table}
}
\chapter{Appendix content Two}
\foreach \x in {1,...,10} {%
\begin{figure}
\caption{Figure caption \x}
\end{figure}
\begin{table}
\caption{Table caption \x}
\end{table}
}
\end{document}

anexo.texplace this line:\addtocontents{toc}{\renewcommand{\cftchapnumwidth}{6em}}and similarly for{lof}. it must be in the file with the appendix material. i know that if it's placed in a "calling" file and the "text" file is called with\include, the\addtocontentsis delayed until after that file has been input; i'm not sure about the ordering if\inputis used, but it's better not to take a chance. – barbara beeton Mar 17 '17 at 13:43.toc(or.lof, etc.) file in the appropriate place. – barbara beeton Mar 17 '17 at 14:35