We report on $p-\Lambda$, $p-\bar{\Lambda}$, $\bar{p}-\Lambda$, and $\bar{p}-\bar{\Lambda}$ correlation functions constructed in central $Au-Au$ collisions at $\sqrt{s_{NN}}=200$ GeV by the STAR experiment at RHIC. The proton and lambda source size is inferred from the $p-\Lambda$ and $\bar{p}-\bar{\Lambda}$ correlation functions. It is found to be smaller than the pion source size also measured by the STAR experiment at smaller transverse masses, in agreement with a scenario of a strong universal collective flow. The $p-\bar{\Lambda}$ and $\bar{p}-\Lambda$ correlation functions, which are measured for the first time, exhibit a large anticorrelation. Annihilation channels and/or a negative real part of the spin-averaged scattering length must be included in the final-state interactions calculation to reproduce the measured correlation function.