For a Lagrangian subbundle L in the Courant algebroid T+T*, the exterior algebroid wedge(L) acts naturally on the de Rham forms Omega. Whenever a transverse Lagrangian M is chosen, we can embed the (graded) algebra of L-forms Omega_L into the (graded) algebra of (graded) differential operators on Omega. There is also a distinguished differential operator on Omega -- the de Rham differential! This setting allow us to apply (a modification of) the Voronov's higher derived bracket method, by which we construct a natural family of brackets on Omega_L. The bracket have arity 0,1,2 and 3 respectively, and are compatible in appropriate sense (that is, they form an L_infinity algebra on Omega_L). In the case, when both L and M are Dirac structures, the L_infinity structure specializes to the differential graded Lie algebra controlling the deformation theory of L. Finally, we will discuss how does the constructed family of brackets on Omega_L depend on the choice of complementary Lagrangian M.