We report the results of our investigation of a fluid-based driven-dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system behavior as it is energized through a progressive increase in the bath’s vibrational acceleration. Depending on the number of drops, the onset of motion of the lattice may take the form of either out-of-phase oscillations or a striking solitary wavelike instability. Theoretical modeling demonstrates that these behaviors may be attributed to different bifurcations at the onset of instability. The results presented here demonstrate the potential and utility of the walking droplet system as a platform for investigating wave-mediated, inertial, nonequilibrium particle dynamics at the macroscale.