A measurement of the top quark mass using events with one charged lepton, missing transverse energy, and jets in the final state, collected by the D0 detector from p[overline p] collisions at sqrt(s)=1.96 TeV at the Fermilab Tevatron collider, is presented. A constrained fit is used to fully reconstruct the kinematics of the events. For every event a top quark mass likelihood is calculated taking into account all possible jet assignments and the probability that an event is signal or background. Lifetime-based identification of b jets is employed to enhance the separation between t[overline t] signal and background from other physics processes and to improve the assignment of the observed jets to the quarks in the t[overline t] hypothesis. We extract a multiplicative jet energy scale (JES) factor in situ, greatly reducing the systematic effect related to the jet energy measurement. In a data sample with an integrated luminosity of 425 pb-1, we observe 230 candidate events, with an estimated background of 123 events, and measure mt=173.7±4.4(stat+JES)-2.0+2.1(syst) GeV. This result represents the first application of the ideogram technique to the measurement of the top quark mass in lepton+jets events.