The high path loss associated with millimeter wave (mmWave) frequency communication can be compensated by large scale antenna arrays such as multiple-input multiple-output (MIMO) systems. The hybrid beamforming architecture which uses fewer radio frequency chains is implemented to reduce power consumption and hardware complexity, while still supporting multi-stream communication. We propose an efficient expectation-maximization (EM)-based mmWave channel estimator for a lens-based hybrid MIMO system with low resolution sampling at the receiver. The lens-based beamformer is investigated to provide increased antenna gain and reduced implementation complexity as the conventional beam selection network is excluded. Low resolution sampling at the analog-to-digital converters is implemented for reduced power consumption. The proposed solution with a robust maximum a posteriori estimator based on the EM algorithm performs better than the conventional EM approach and minimum mean square error baselines in medium to high signal-to-noise ratio regions.