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 $L=[Iotimes 1]$ and the spin angular momentum of $S=1/2$.
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