Light propagation in optical lattices of driven cold atoms exhibits non-Hermitian degeneracies when the first-order modulation amplitudes of real and imaginary parts of the probe susceptibility are manipulated to be balanced. At these degeneracies, one may observe complete unidirectional reflectionless light propagation. This strictly occurs with no gain and can be easily tuned and fully reversed as supported by the transfer-matrix calculations and explained via a coupled-mode analysis.