  We characterize strong continuity of general operator semigroups on some
Lebesgue spaces. In particular, a characterization of strong continuity of
weighted composition semigroups on classical Hardy spaces and weighted Bergman
spaces with regular weights is given. As applications, our result improves the
results of Siskakis, A. G. \cite{AG1} and K\"{o}nig, W. \cite{K} and answers a
question of Siskakis, A. G. proposed in \cite{AG4}. We also characterize
strongly continuous semigroups of weighted composition operators on weighted
Bergman spaces in terms of abelian intertwiners of multiplication operator
$M_z$.
