Input to the shortest lagrangian path (SLP) problem consists of the following: (a) road network dataset (modeled as a time-varying graph to capture its temporal variation in traffic), (b) a source-destination pair and, (c) a departure-time (\(t_{dep}\)). Given the input, the goal of the SLP problem is to determine a fastest path between the source and destination for the departure-time \(t_{dep}\) (at the source). The SLP problem has value addition potential in the domain of urban navigation. SLP problem has been studied extensively in the research literature. However, almost all of the proposed algorithms are essentially serial in nature. Thus, they fail to take full advantage of the increasingly available multi-core (and multi-processor) systems. However, developing parallel algorithms for the SLP problem is non-trivial. This is because SLP problem requires us to follow Lagrangian reference frame while evaluating the cost of a candidate path. In other words, we need to relax an edge (whose cost varies with time) only for the time at which the candidate path (from source) arrives at the head node of the edge. Otherwise, we would generate meaningless labels for nodes. This constraint precludes use of any label correcting based approaches (e.g., parallel version of Delta-Stepping at its variants) as they do not relax edges along candidate paths. Lagrangian reference frame can be implemented in label setting based techniques, however, they are hard to parallelize. In this paper, we propose a novel multi-threaded label setting algorithm called IMRESS which follows Lagrangian reference frame. We evaluate IMRESS both analytically and experimentally. We also experimentally compare IMRESS against related work to show its superior performance.