A lignin composite reinforced with 30% flax fibers at two levels of relative humidity, 34 and 66%, was used in this study. The nonlinearity of the composite was analyzed by studying the degradation of its modulus and the development of viscoelastic and viscoplastic strains. The reduction in the modulus of lignin-based composites in tension starts before the maximum in the stress–strain curve is reached and can be as large as 50%. With increasing relative humidity, these effects are slightly magnified. The time-dependent phenomena in tension were examined in short-term creep and strain recovery tests, demonstrating a rather high viscoplastic strain in lignin composites. Both viscoelastic and viscoplastic strains are larger at a higher relative humidity.