A search is presented for W' bosons in events with an electron or muon and large missing transverse momentum, using proton-proton collision data at (\sqrt{s}) = 13 TeV collected with the CMS detector in 2015 and corresponding to an integrated luminosity of 2.3 fb⁻¹. No evidence of an excess of events relative to the standard model expectations is observed. For a W' boson described by the sequential standard model, upper limits at 95% confidence level are set on the product of the production cross section and branching fraction and lower limits are established on the new boson mass. Masses below 4.1 TeV are excluded combining electron and muon decay channels, significantly improving upon the results obtained with the 8 TeV data. Exclusion limits at 95% confidence level on the product of the W' production cross section and branching fraction are also derived in combination with the 8 TeV data. Finally, exclusion limits are set for the production of generic W' bosons decaying into this final state using a model-independent approach.