We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggest that with the appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L \approx 8–14$ fm. Of particular importance is our derivation and numerical verification of three-body analogs of “i-periodic” twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.