  In order to clarify the nature of hypernuclear low-lying states, we carry out
a comprehensive study for the structure of
$^{144-154}_{~~~~~~~~\Lambda}$Sm-hypernuclei, which exhibit a transition from
vibrational to rotational characters as the neutron number increases. To this
end, we employ a microscopic particle-core coupling scheme based on a covariant
density functional theory. We find that the positive-parity ground-state band
in the hypernuclei shares a similar structure to that of the corresponding core
nucleus. That is, regardless of whether the core nucleus is spherical or
deformed, each hypernuclear state is dominated by the single configuration of
the $\Lambda$ particle in the $s_{1/2}$ state ($\Lambda s_{1/2}$) coupled to
one core state of the ground band. In contrast, the low-lying negative-parity
states mainly consist of $\Lambda p_{1/2}$ and $\Lambda p_{3/2}$ configurations
coupled to plural nuclear core states. We show that, while the mixing amplitude
between these configurations is negligibly small in spherical and
weakly-deformed nuclei, it strongly increases as the core nucleus undergoes a
transition to a well-deformed shape, being consistent with the Nilsson wave
functions. We demonstrate that the structure of these negative-parity states
with spin $I$ can be well understood based on the $LS$ coupling scheme, with
the total orbital angular momentum of $L=[I\otimes 1]$ and the spin angular
momentum of $S=1/2$.
