Low-emissions can-annular gas turbines are prone to develop low-frequency self-excited thermoacoustic oscillations. Such oscillations arise from the coupling between adjacent combustors and can increase wear and thermal stresses. In this experimental study, we explore the mutual synchronization of two thermoacoustic oscillators (i.e., two model combustors) interacting via dissipative and time-delayed coupling, as introduced via a cross-talk section. Unlike most previous studies, our study makes use of a turbulent lean-premixed flame in each combustor, bringing the system configuration closer to that of practical gas turbines. Using stationary and transient measurements, we examine the effect of the cross-talk diameter and length so as to gain insight into the effect of dissipative and time-delayed coupling. We find that strengthening the dissipative coupling promotes mutual synchronization, but that weakening the dissipative coupling leads to weakly coupled or desynchronized oscillations. On operating the two combustors at different conditions, we find a significant reduction in their overall oscillation amplitude for some coupling conditions. On varying the combustor length and examining the transient response, we find elaborate changes in the pressure-heat-release-rate coupling, spontaneous mode transitions between coupled thermoacoustic modes, and the emergence of a rhomboid structure in the phase plane owing to the coexistence of in-phase and out-of-phase synchronization. In the combustion community, these two types of synchronization are known to be associated with push-push modes and push-pull modes. These findings offer new insight into the mutual synchronization of low-frequency, self-excited thermoacoustic oscillations in can-annular gas turbines, paving the way for the development of improved control strategies. Published under license by AIP Publishing.