We develop both relativistic mean field and beyond approaches for hypernuclei with possible quadrupole-octupole deformation or pear-like shapes based on relativistic point-coupling energy density functionals. The symmetries broken in the mean-field states are recovered with parity, particle-number, and angular momentum projections. We take $^{21}_Lambda$Ne as an example to illustrate the method, where the $Lambda$ hyperon is put on one of the two lowest-energy orbits (labeled as $Lambda_s, Lambda_p$), respectively. We find that the $Lambda$ hyperon in both cases disfavors the formation of a reflection-asymmetric molecular-like $^{16}$O$+alpha$ structure in $^{20}$Ne, which is consistent with the Nilsson diagram for the hyperon in $(beta_2, beta_3)$ deformation plane. In particular, we show that the negative-parity states with the configuration $^{20}$Ne($K^pi=0^-)otimes Lambda_s$ are close in energy to those with the configuration $^{20}$Ne($K^pi=0^+)otimes Lambda_p$, even though they have very different structures. The $Lambda_s$ ($Lambda_p$) becomes more and more concentrated around the bottom (top) of the pear with the increase of octupole deformation.
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