We have searched for the Cabibbo-suppressed decay $Lambda_c^+tophi ppi^0$ in $e^+e^-$ collisions using a data sample corresponding to an integrated luminosity of 915 $rm fb^{-1}$. The data were collected by the Belle experiment at the KEKB $e^+e^-$ asymmetric-energy collider running at or near the $Upsilon(4S)$ and $Upsilon(5S)$ resonances. No significant signal is observed, and we set an upper limit on the branching fraction of $mathcal{B}(Lambda_c^+to phi ppi^0) <15.3times10^{-5}$ at 90% confidence level. The contribution for nonresonant $Lambda_c^+to K^+K^- ppi^0$ decays is found to be consistent with zero and the corresponding upper limit on its branching fraction is set to be $mathcal{B}(Lambda_c^+to K^+K^-ppi^0)_{rm NR} <6.3times10^{-5} $ at 90% confidence level. We also measure the branching fraction for the Cabibbo-favored decay $Lambda_c^+to K^-pi^+ppi^0$; the result is $mathcal{B}(Lambda_c^+to K^-pi^+ppi^0)= (4.42pm0.05, (rm stat.) pm 0.12, (rm syst.) pm 0.16, (mathcal{B}_{rm Norm}))%$, which is the most precise measurement to date. Finally, we have searched for an intermediate hidden-strangeness pentaquark decay $P^+_stophi p$. We see no evidence for this intermediate decay and set an upper limit on the product branching fraction of ${cal B}(Lambda_c^+to P^+_s pi^0)times {cal B}(P^+_stophi p) <8.3times 10^{-5}$ at 90% confidence level.
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