[Background] The hyperon impurity effect in nuclei has been extensivelystudied in different mean-field models. Recently, there is a controversy aboutwhether the $\Lambda$ hyperon is more tightly bound in the normal deformed (ND)states than that in the superdeformed (SD) states.[Purpose] This article isaimed to provide a beyond-mean-field study of the low-lying states ofhypernuclei with shape coexistence and to shed some light on thecontroversy.[Method] The models of relativistic mean-field and beyond based ona relativistic point-coupling energy functional are adopted to study thelow-lying states of both $^{37}_\Lambda$Ar and $^{36}$Ar. The wavefunctions oflow-lying states are constructed as a superposition of a set of relativisticmean-field states with different values of quadrupole deformation parameter.The projections onto both particle number and angular momentum areconsidered.[Results] The $\Lambda$ binding energies in both ND and SD states of$^{37}_{\Lambda}$Ar are studied in the case of the $\Lambda$ hyperon occupying$s, p$, or $d$ state in the spherical limit, respectively. For comparison, foursets of nucleon-hyperon point-coupling interactions are used respectively.Moreover, the spectra of low-lying states in $^{36}$Ar and$^{37}_{\Lambda_s}$Ar are calculated based on the same nuclear energy densityfunctional. The results indicate that the SD states exist in$^{37}_{\Lambda}$Ar for all the four effective interactions. Furthermore, the$\Lambda_s$ reduces the quadrupole collectivity of ND states to a greaterextent than that of SD states. For $^{37}_{\Lambda}$Ar, the beyond-mean-fielddecreases the $\Lambda_s$ binding energy of the SD state by 0.17 MeV, but italmost has no effect on that of the ND state. [Conclusions] In$^{37}_{\Lambda_s}$Ar, the $\Lambda_p$ and $\Lambda_d$ binding energies of theSD states ...
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