Thermal properties of low-density neutron matter are investigated by lattice calculation with nuclear effective field theory without pions up to the next-to-leading order. The 1S0 pairing gap is extracted near zero temperature at low densities. We find that the pairing gap is smaller than the BCS approximation with the conventional NN potentials, but not as small as those by various many-body calculations beyond BCS approximation. Our result is consistent with the recent Green's Function Monte Carlo calculation within the statistical errors. The critical temperature of the normal-to-superfluid phase transition and the pairing temperature scale are also extracted at low densities, and the phase diagram is given. We find that the physics of low-density neutron matter is clearly identified as being BCS-BEC crossover.