This article aims to explore synergies between Lean Production (LP) and Six Sigma principles in order to propose a Lean Six Sigma (LSS) framework for continuous and incremental improvement in the oil and gas sector. The Three-Dimensional LSS Framework seeks to provide various combinations about the integration between LP principles, DMAIC cycle and PDCA cycle to support operations management needs. Design/methodology/approach - The research method is composed of two main steps: (i) diagnostic of current problems and proposition of a conceptual framework that qualitatively integrates synergistic aspects of LP and Six Sigma; and (ii) analysis of the application of the construct through semi-structured interviews with leaders from oil and gas companies to assess and validate the proposed framework. Findings - As a result, a conceptual framework of LSS is developed contemplating the integration of LP and Six Sigma and providing a systemic and holistic approach to problemsolving through continuous and incremental improvement in the oil and gas sector. Originality/value - This research is different from previous studies because it integrates LP principles, DMAIC and PDCA cycles into a unique framework that fulfils a specific need of oil and gas sector. It presents a customized LSS framework that guides wastes and costs reduction, while enhances quality and reduces process variability to elevate efficiency in operations management of this sector. The paper type is an original research that present new and original scientific findings.N/