Spin-transfer observables for p p-->Lambda Lambda have been measured using a transversely polarized frozen-spin target and a beam momentum of 1.637 GeV/c. Current models of the reaction near threshold are in good agreement with existing measurements performed with unpolarized particles in the initial state but produce conflicting predictions for the spin-transfer observables Dnn and Knn (the normal-to-normal depolarization and polarization transfer), which are measurable only with polarized target or beam. Measurements of Dnn and Knn presented here are found to be in disagreement with predictions from these models.