Results are presented from a search for the production of a heavy gauge boson W' decaying into a top and a bottom quark, using a data set collected by the CMS experiment at sqrt(s) = 8 TeV and corresponding to an integrated luminosity of 19.5 inverse femtobarns. Various models of W'-boson production are studied by allowing for an arbitrary combination of left- and right-handed couplings. The analysis is based on the detection of events with a lepton (e, mu), jets, and missing transverse energy in the final state. No evidence for W'-boson production is found and 95% confidence level upper limits on the production cross section times branching fraction are obtained. For W' bosons with purely right-handed couplings, and for those with left-handed couplings assuming no interference effects, the observed 95% confidence level limit is M(W') > 2.05 TeV. For W' bosons with purely left-handed couplings, including interference effects, the observed 95% confidence level limit is M(W') > 1.84 TeV. The results presented in this paper are the most stringent limits published to date.