{gamma} rays were measured at several angles in both singles and coincidence mode in the {sup 119}Sn({alpha},n{gamma}){sup 122}Te reaction at 15 MeV on a thick target. Lifetimes of excited states in {sup 122}Te were determined from a Monte Carlo Doppler shift attenuation method (DSAM) analysis of the Doppler broadened lines shapes of {gamma} rays de-exciting the levels. A comparison of several deduced lifetimes with recent results obtained with the (n,n{sup '}) reaction allowed us to validate the choice of a parameter used to calculate the contribution of the side feeding times. The ingredients of the DSAM line-shape analysis (stopping power, description of instrumental line shapes, and side feeding evaluation) are presented in some detail. It is concluded that with proper treatment of side feeding, a DSAM line-shape analysis of peaks in singles or coincidence spectra obtained following the ({alpha},n{gamma}) reaction is able to provide rather accurate values for the lifetimes of levels with low and medium spins.