A novel Monte Carlo technique has been developed to determine lifetimes of excited states in the tens-to-hundreds femtoseconds range in products of low-energy heavy-ion binary reactions, with complex velocity distributions. The method is based on a detailed study of Doppler-broadened gamma -ray lineshapes. Its relevance is demonstrated in connection with the ^{18}text {O}(7.0, text {MeV/u})+,^{181}text {Ta} experiment, performed at GANIL with the AGATA+VAMOS+PARIS setup, to study neutron-rich O, C, N, ... nuclei. Excited states in ^{17}text {O} and ^{19}text {O}, with known lifetimes, are used to validate the method over the sim 20{-}400,text {fs} lifetime-sensitivity range. Emphasis is given to the unprecedented position resolution provided by gamma -tracking arrays, which turns out to be essential for reaching the required accuracy in Doppler-shift correction. The technique is anticipated to be an important tool for lifetime investigations in exotic neutron-rich nuclei, produced with intense ISOL-type beams.