Using 567 $pb^{-1}$ of data collected with the BESIII detector at a center-of-mass energy of $sqrt{s}=$ 4.599 $GeV$, near the $Lambda_{c}^{+}Lambda_{c}^{-}$ threshold, we study the singly Cabibbo-suppressed decays $Lambda_c^{+}to ppi^{+}pi^{-}$ and $Lambda_c^{+}to pK^{+}K^{-}$. By normalizing with respect to the Cabibbo-favored decay $Lambda_c^{+}to pK^{-}pi^{+}$, we obtain ratios of branching fractions: $frac{mathcal{B}(Lambda_c^{+}to ppi^{+}pi^{-})}{mathcal{B}(Lambda_c^{+}to pK^{-}pi^{+})}$ = $(6.70 pm 0.48 pm 0.25)%$, $frac{mathcal{B}(Lambda_c^{+}to pphi)}{mathcal{B}(Lambda_c^{+}to pK^{-}pi^{+})}$ = $(1.81 pm 0.33 pm 0.13)%$, and $frac{mathcal{B}(Lambda_c^{+}to pK^{+}K^{-}_{text{non-}phi})}{mathcal{B}(Lambda_c^{+}to pK^{-}pi^{+})}$ = $(9.36 pm 2.22 pm 0.71)times10^{-3}$, where the uncertainties are statistical and systematic, respectively. The absolute branching fractions are also presented. Among these measurements, the decay $Lambda_c^{+}to ppi^{+}pi^{-}$ is observed for the first time, and the precision of the branching fraction for $Lambda_c^{+}to pK^{+}K^{-}_{text{non-}phi}$ and $Lambda_c^{+}to pphi$ is significantly improved.
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