10 pages, 7 figures, and 4 Tables. Accepted for publication in MNRAS ; International audience ; One of the most accurate models currently used to represent the gravity field of irregular bodies is the polyhedral approach. In this model, the mass of the body is assumed to be homogeneous, which may not be true for a real object. The main goal of the present paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layers) of asteroid (21) Lutetia, an object that recent results from space probe suggest being at least partially differentiated. The Mascon gravity approach used in the present work, consists of dividing each tetrahedron into eight parts to calculate the gravitational field around the asteroid. The zero-velocity curves show that the greatest displacement of the equilibrium points occurs in the position of the E4 point for the four-layers structure and the smallest one occurs in the position of the E3 point for the three-layers structure. Moreover, stability against impact shows that the planar limit gets slightly closer to the body with the four-layered structure. We then investigated the stability of orbital motion in the equatorial plane of (21) Lutetia and propose numerical stability criteria to map the region of stable motions. Layered structures could stabilize orbits that were unstable in the homogeneous model.