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The Shastry-Sutherland lattice (SSL) comprises a two-dimensional orthogonal arrangement of spin dimers. By varying the ratio of intra-dimer and inter-dimer interactions, the rich phase diagram can emerge, including exotic quantum phases. Single-ion and exchange magnetic anisotropies can further diversify the phased diagram and lead to quantum states beyond the toy model of antiferromagnetic Heisenberg SSL. For example, a quantum critical point was reached by applying a magnetic field in BaNd₂ZnS₅ SSL [1]. At zero field, it presents a 2Q non-collinear magnetic order. When Nd³⁺ is replaced with Ce³⁺, no magnetic order is detected until 40 mK. To understand the magnetic disorder in BaCe₂ZnS₅ SSL, we have studied its local site magnetic anisotropy my polarized neutron diffraction, crystal electric field excitations, magnetic dimer excitations through inelastic neutron scattering. In this presentation, I will introduce our latest data modeling results and make a comparison between the field-induced disorder in  BaNd₂ZnS₅ and the magnetic disorder observed in BaCe₂ZnS₅.