The dynamic transitions preceding lean blowout were investigated experimentally in a laboratory scale turbulent combustor by systematically varying the flow Reynolds number (Re). Previous studies on combustor dynamics have shown that the onset of large-amplitude, combustion-driven oscillations is, at times, presaged by intermittent bursts of high-amplitude periodic pressure pulsations. These intermittent bursts appear in a near random fashion amidst regions of aperiodic low-amplitude fluctuations, provided the underlying flow-field is turbulent. In the present study, we show that intermittent burst oscillations are also observed in combustors close to the lean blowout limit. We show that such intermittent oscillations emerge through the establishment of homoclinic orbits in the phase space of pressure oscillations. The formation of such orbits points to the complex nature of the interaction between the hydrodynamics and acoustic subsystems, which operate over a range of different time scales. High-speed flame images reveal that the intermittent states observed prior to lean blowout correspond to aperiodic detachment of the flame from the bluff-body lip. These findings are consistent with other reports of possibly intermittent states in the literature.