We calculate the longitudinal-acoustic phonon scattering rate for a vertical double quantum dot (DQD) system and show that a strong modulation of the single-electron excited states lifetime can be induced by an external magnetic field. The results are obtained for typical realistic devices using a Fermi golden rule approach and a three-dimensional description of the electronic quantum states. The DQDs considered are characterized by a weak lateral confinement and the longitudinal-phonon scattering represents the dominant source of decoherence, its tunable suppression can be a valuable tool for an experimental measure of electron-states lifetimes and serve as a signature for coherent delocalization of electrons in the DQD. (C) 2004 Elsevier B.V. All rights reserved.