We present a measurement of forward-backward asymmetry in top quark-antiquark production in proton-antiproton collisions in the final state containing a lepton and at least four jets. Using a dataset corresponding to an integrated luminosity of $5.4\,\mathrm {fb}^{-1}$, collected by the \DZ\ experiment at the Fermilab Tevatron Collider, we measure the \ttbar\ forward-backward asymmetry to be $(9.2 \pm 3.7)$% at the reconstruction level. When corrected for detector acceptance and resolution, the asymmetry is found to be $(19.6 \pm 6.5)$%. We also measure a corrected asymmetry based on the lepton from a top quark decay, found to be $(15.2 \pm 4.0)$%. The results are compared to predictions based on the next-to-leading-order QCD generator {\sc mc@nlo}. The sensitivity of the measured and predicted asymmetries to the modeling of gluon radiation is discussed.