Let G be a compact Lie group and let M = G/H be a G-homogeneous space, equipped with an invariant metric. We prove that the spectral norm of any compact exact Lagrangian submanifold of the cotangent bundle T²M is bounded in terms of the diameter and dimension of G. Our proof is by sheaf theoretical methods; it recovers some results of Shelukhin and gives some other cases. This is a joint work in progress with Nicolas Vichery.