  We consider low-energy nucleons at next-to-next-to-leading order in lattice
chiral effective field theory. Three-body interactions first appear at this
order, and we discuss several methods for determining three-body interaction
coefficients on the lattice. We compute the energy of the triton and low-energy
neutron-deuteron scattering phase shifts in the spin-doublet and spin-quartet
channels using Luescher's finite volume method. In the four-nucleon system we
calculate the energy of the alpha particle using auxiliary fields and
projection Monte Carlo.
