  We use high-order cumulants to investigate the Lee-Yang zeros of generating
functions of dynamical observables in open quantum systems. At long times the
generating functions take on a large deviation form with singularities of the
associated cumulant generating functions - or dynamical free energies -
signifying phase transitions in the ensemble of dynamical trajectories. We
consider a driven three-level system as well as the dissipative Ising model.
Both systems exhibit dynamical intermittency in the statistics of quantum
jumps. From the short-time behavior of the dynamical Lee-Yang zeros we identify
critical values of the counting field which we attribute to the observed
intermittency and dynamical phase co-existence. Furthermore, for the
dissipative Ising model we construct a trajectory phase diagram and estimate
the value of the transverse field where the stationary state changes from being
ferromagnetic (inactive) to being paramagnetic (active).
