We analyse holomorphic discs on Lagrangian SU(2)-orbits in a family of quasihomogeneous threefolds of SL(2;C), previously studied by Evans-Lekili, introducing several techniques that should be applicable to wider classes of homogeneous Lagrangians. By studying the closed-open map we place strong restrictions on the self-Floer cohomology of these Lagrangians, which we then compute using the Biran-Cornea pearl complex.