The production of eta and eta' mesons is studied in proton -proton and proton -lead collisions collected with the LHCb detector. Proton -proton collisions are studied at center -of -mass energies of 5.02 and 13 TeV and proton -lead collisions are studied at a center -of -mass energy per nucleon of 8.16 TeV. The studies are performed in center -of -mass (c.m.) rapidity regions 2.5 < y(c.m.) < 3.5 (forward rapidity) and -4.0 < y(c.m.) < -3.0 (backward rapidity) defined relative to the proton beam direction. The eta and eta' production cross sections are measured differentially as a function of transverse momentum for 1.5 < p(T) < 10 GeV and 3 < p(T) < 10 GeV, respectively. The differential cross sections are used to calculate nuclear modification factors. The nuclear modification factors for eta and eta' mesons agree at both forward and backward rapidity, showing no significant evidence of mass dependence. The differential cross sections of eta mesons are also used to calculate eta/pi 0 cross-section ratios, which show evidence of a deviation from the world average. These studies offer new constraints on mass -dependent nuclear effects in heavy -ion collisions, as well as eta and eta' meson fragmentation.