The relaxation to equilibrium of lattice systems with long-range interactions is investigated. The timescales involved depend polynomially on the system size, potentially leading to diverging equilibration times. A kinetic equation for long-range lattices is proposed, which explain these timescales as well as a threshold in the interaction range reported in [Phys. Rev. Lett. 110, 170603 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.170603]. Non-Markovian effects are shown to play an important role in the relaxation of systems of up to thousands of particles.