Over the past years, we have performed one of the most extensive study of the young (lambda)-Orionis star forming region, combining photometric data from the xray to the mid-IR, as well as wide field and high spatial resolution imaging. This effort allowed us to identify hundreds of very low mass stars, brown dwarfs and isolated planetary mass candidate members in the three clusters present in this region: Collinder 69, Barnard 30 and Barnard 35, with the ultimate aim to perform a detailed study of the very low mass end of the IMF from the core of the clusters to their periphery. We now propose to use the unique capabilities of IMACS to perform spectroscopic follow-up observations of these candidates members. The spectra will allow us to: i) determine the spectral type - and therefore the T_eff - of our candidates; ii) assess their membership to the clusters using various complementary diagnostics (presence or absence of H(alpha), gravity sensitive lines such as K I, Na I); iii) draw a definitive census of the IMF of the cluster over the entire mass spectrum, from its core to its edges. The proposed observations will allow us to make a unique comprehensive study of the IMF of a nearby young massive cluster down to M=15~20 M_Jup and of the properties (discs, accretion) of its substellar members, and a benchmark result for all the models of formation and evolution.