Two-particle correlations are presented for K_S⁰, Λ, and Λ‾ strange hadrons as a function of relative momentum in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset corresponds to an integrated luminosity of 0.607nb⁻¹ and was collected using the CMS detector at the CERN LHC. These correlations are sensitive to quantum statistics and to final-state interactions between the particles. The source size extracted from the K_S⁰K_S⁰ correlations is found to decrease from 4.6 to 1.6 fm in going from central to peripheral collisions. Strong interaction scattering parameters (i.e., scattering length and effective range) are determined from the ΛK_S⁰ and ΛΛ (including their charge conjugates) correlations using the Lednický–Lyuboshitz model and are compared to theoretical and other experimental results.