The study of the detonation physics presents a big challenge for the computational fluid dynamics (CFD) due to the variety of characteristic scales at stake, the presence of large pressure ratios and a complex competition occurring between flow discontinuities and chemistry. For the simulation of compressible and reacting flows, the hybrid lattice Boltzmann method (LBM) has recently proven to be an increasingly convincing and highly efficient alternative to conventional CFD methods. However, no LBM scheme has been able to correctly simulate simultaneous shock waves and chemical reactions so far, which is yet crucial for the detonations. The reason lies in two difficulties faced by these approaches: the conservativity of the model and its numerical stability. In the present work, the construction of a stable conservative scheme for the hybrid LBM is proposed for numerical simulations of reactive multi-species compressible flows. This work is an extension of the discretization of the energy equation in its conservative form recently proposed for the hybrid LBM. It relies on a linear equivalence with the entropy equation which, as a characteristic variable of the Euler system, ensures a decoupling of the energy equation with the LBM. The present extension allows the total energy and the mass of all the species to be conserved by the use of new discretizations inspired by a MUSCL-TVD scheme. They are validated on several test cases: the convection of inert species, a shock tube with two ideal gases and one- and two-dimensional detonations. The physical instabilities expected by stability analyses of detonation waves are perfectly recovered, further extending the capabilities of the LBM to faithfully simulate compressible reacting flows.