breakable in tcolorbox not breaking

Question

\documentclass[12pt, a4paper, UTF8, scheme = plain, twoside]{ctexart}
\usepackage{amsmath}
\usepackage{enumerate}
\renewcommand{\labelenumi} {(\roman{enumi})}
\renewcommand{\labelenumii}{(\alph{enumii})}
\usepackage[top=0.5cm,left=0.5cm,right=0.5cm,bottom=2.28cm]{geometry}
\usepackage{hyperref}
\usepackage{graphicx}
\pdfsuppressptexinfo=-1
\usepackage{lipsum}
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%       - Fancyhdr -    %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{fancyhdr}
\usepackage{totpages}
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{tcolorbox}
\tcbuselibrary{skins,xparse,breakable}
\tcbset{%
    colback      = white,
    tikz         = {opacity=0.1,transparency group},
    colframe     = black,
    title filled = false,
    colbacktitle = white,
}%%
\NewTColorBox[
    ]{question}{ O{}mo }{
    fonttitle                 = \bfseries,
    coltitle                  =  black,
    title                     = #2,
    before lower              = {\textbf{Solution\quad}},
    #1
}%
%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%
%%%  DOC Begins   %%%
%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\thispagestyle{empty}
\begin{question}
% \lipsum[4]
Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah 
\tcblower
\[
    \lambda = 2\times10^5
    \qquad
    l_0 = 2
\]
% \lipsum[4]
Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah Blah \lipsum[4-10]
\end{question}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%

Why does the breakable not working in this case?

Answer 1

As said in comments, you should not just load breakable, you must tell the box if it is allowed to be breakable.

I commented the tikz = {opacity=0.1,transparency group} to make your example visible and I also added the {Title} to your {question} environment. As you created a \NewTColorBox with two arguments, the first optional but the second doesn't seem to be ({question}{ O{}mo } and title = #2,).

A MWE follows.

\documentclass[12pt, a4paper, UTF8, scheme = plain, twoside]{ctexart}
\usepackage{amsmath}
\usepackage{enumerate}
\renewcommand{\labelenumi} {(\roman{enumi})}
\renewcommand{\labelenumii}{(\alph{enumii})}
\usepackage[top=0.5cm,left=0.5cm,right=0.5cm,bottom=2.28cm]{geometry}
\usepackage{hyperref}
\usepackage{graphicx}
\pdfsuppressptexinfo=-1
\usepackage{lipsum}
\usepackage{tcolorbox}
\tcbuselibrary{skins,xparse,breakable}
\tcbset{%
  colback      = white,
  %tikz         = {opacity=0.1,transparency group},
  colframe     = black,
  title filled = false,
  colbacktitle = white,
  breakable
}
\NewTColorBox[
]{question}{ O{}mo }{
  fonttitle    = \bfseries,
  coltitle     =  black,
  title        = #2,
  before lower = {\textbf{Solution\quad}},
  breakable,
  #1
}
\begin{document}
\thispagestyle{empty}
\begin{question}{Title}
  \lipsum[1-3]
  \tcblower
  \[
  \lambda = 2\times10^5
  \qquad
  l_0 = 2
  \]
  \lipsum[4-10]
\end{question}
\end{document}