Combining adaptive and robust optimization in radiation therapy has the potential to mitigate the negative effects of both intrafraction and interfraction uncertainty over a fractionated treatment course. A previously developed adaptive and robust radiation therapy (ARRT) method for lung cancer was demonstrated to be effective when the sequence of breathing patterns was well-behaved. In this paper, we examine the applicability of the ARRT method to less well-behaved breathing patterns. We develop a novel method to generate sequences of probability mass functions that represent different types of drift in the underlying breathing pattern. Computational results derived from applying the ARRT method to these sequences demonstrate that the ARRT method is effective for a much broader class of breathing patterns than previously demonstrated.