We report measurements of the branching fractions of the decays $Lambda^+_ctoSigma^+pi^-pi^+$, $Lambda^+_ctoSigma^0pi^+pi^0$ and $Lambda^+_ctoSigma^+pi^0pi^0$ relative to the reference channel $Lambda^+_cto pK^-pi^+$. The analysis is based on the full data sample collected at and close to $Upsilon(4S)$ resonance by the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider corresponding to the integrated luminosity of 711 fb$^{-1}$. We measure ${cal B}(Lambda^+_crightarrowSigma^+pi^-pi^+)/{cal B}(Lambda^+_cto pK^-pi^+) = 0.706~pm 0.003~pm 0.029$, ${cal B}(Lambda^+_crightarrowSigma^0pi^+pi^0)/{cal B}(Lambda^+_cto pK^-pi^+) = 0.491~pm 0.005~pm 0.028$ and ${cal B}(Lambda^+_crightarrowSigma^+pi^0pi^0)/{cal B}(Lambda^+_cto pK^-pi^+) = 0.198~pm 0.006~pm 0.016$. The listed uncertainties are statistical and systematic, respectively.