AI business process applications automate high-stakes business decisions where there is an increasing demand to justify or explain the rationale behind algorithmic decisions. Business process applications have ordering or constraints on tasks and feature values that cause lightweight, model-agnostic, existing explanation methods like LIME to fail. In response, we propose a local explanation framework extending LIME for explaining AI business process applications. Empirical evaluation of our extension underscores the advantage of our approach in the business process setting.