Autonomous agents are often required to plan under multiple objectives whose preference ordering varies based on context. The agent may encounter multiple contexts during its course of operation, each imposing a distinct lexicographic ordering over the objectives, with potentially different reward functions associated with each context. Existing approaches to multi-objective planning typically consider a single preference ordering over the objectives, across the state space, and do not support planning under multiple objective orderings within an environment. We present Contextual Lexicographic Markov Decision Process (CLMDP), a framework that enables planning under varying lexicographic objective orderings, depending on the context. In a CLMDP, both the objective ordering at a state and the associated reward functions are determined by the context. We employ a Bayesian approach to infer a state-context mapping from expert trajectories. Our algorithm to solve a CLMDP first computes a policy for each objective ordering and then combines them into a single context-aware policy that is valid and cycle-free. The effectiveness of the proposed approach is evaluated in simulation and using a mobile robot.