Two -particle Bose-Einstein momentum correlation functions are studied for charged-hadron pairs in lead -lead collisions at a center -of -mass energy per nucleon pair of .'/sNN = 5.02 TeV. The data sample, containing 4.27 x 109 minimum bias events corresponding to an integrated luminosity of 0.607 nb-1, was collected by the CMS experiment in 2018. The experimental results are discussed in terms of a Levy-type source distribution. The parameters of this distribution are extracted as functions of particle pair average transverse mass and collision centrality. These parameters include the Levy index or shape parameter alpha, the Levy scale parameter R, and the correlation strength parameter lambda. The source shape, characterized by alpha, is found to be neither Cauchy nor Gaussian, implying the need for a full Levy analysis. Similarly to what was previously found for systems characterized by Gaussian source radii, a hydrodynamical scaling is observed for the Levy R parameter. The lambda parameter is studied in terms of the core -halo model.