We investigated the swelling of a thin film of lamellae-forming poly(styrene-b-butadiene) in cyclohexane vapor. The vapor pressure and thus the degree of swelling of the film are increased in a stepwise manner using a custom-built sample cell. The resulting structural changes during and after each step were followed in situ using time-resolved grazing-incidence small-angle X-ray scattering (GISAXS). During the first step, the lamellar thickness increases strongly, before it decreases again. At the same time, the full width at half-maximum (FWHM) of the diffuse Bragg reflection along the film normal has a sharp maximum. These observations point to the formation of new lamellae. During the subsequent swelling steps, the lamellar thickness overshoots only weakly. The behavior thus resembles qualitatively our previous results on a similar thin film during swelling in saturated vapor of cyclohexane; however, it deviates from earlier theoretical predictions. We propose a theory that is quantitatively correct for the description of the dependence of the lamellar thickness on the polymer volume fraction in the late stage of the swelling steps.