  We propose a mechanism in which the lightness of Higgs boson and the
smallness of CP-violation are correlated based on the Lee model, namely the
spontaneous CP-violation two-Higgs-doublet-model. In this model, the mass of
the lightest Higgs boson $m_h$ as well as the quantities $K$ and $J$ are
$\propto t_{\beta}s_{\xi}$ in the limit $t_{\beta}s_{\xi}\rightarrow0$ (see
text for definitions of $t_\beta$ and $\xi$), namely the CP conservation limit.
Here $K$ and $J$ are the measures for CP-violation effects in scalar and Yukawa
sectors respectively. It is a new way to understand why the Higgs boson
discovered at the LHC is light. We investigated the important constraints from
both high energy LHC data and numerous low energy experiments, especially the
measurements of EDMs of electron and neutron as well as the quantities of
B-meson and kaon. Confronting all data, we found that this model is still
viable. It should be emphasized that there is no standard-model limit for this
scenario, thus it is always testable for future experiments. In order to pin
down Lee model, it is important to discover the extra neutral and charged Higgs
bosons and measure their CP properties and the flavor-changing decays. At the
LHC with $\sqrt{s}=14\textrm{TeV}$, this scenario is favored if there is
significant suppression in the $b\bar{b}$ decay channel or any vector boson
fusion (VBF), V+H production channels. On the contrary, it will be disfavored
if the signal strengths are standard-model-like more and more. It can be easily
excluded at $(3\sim5)\sigma$ level with several $\textrm{fb}^{-1}$ at future
$e^+e^-$ colliders, via the accurately measuring the Higgs boson production
cross sections.
