We present simulations of laboratory-scale Low Swirl Burner (LSB) flames in order to develop a characterization of the interaction of thermal/diffusive unstable flames with turbulence at the correct scales of laboratory experiments. A Lagrangian diagnostic was developed to overcome the pitfalls of traditional Eulerian analysis techniques when applied to cellular flame systems, including the lack of a well-defined measure of "flame progress" and the time-dependent strain and curvature fields that evolve at scales that are faster than the residence time in the flame zone. An integrated measure of consumption along the pathlines was shown to serve as a generalized analog of the Eulerian-computed consumption-based burning speed. The diffusive fuel flux divergence along the pathlines was shown to correlate directly with integrated consumption rate. Insights gained through the Lagrangian diagnostic analysis served as the underpinning of a new procedure to interpret OH-PLIF images from the LSB experiment. This new diagnostic is able to provide a more physically meaningful approximation to the "flame surface area" than traditional approaches based on PIV processing. Published by Elsevier Inc. on behalf of The Combustion Institute.