Lean Six Sigma combines the two methodologies. First, Lean methodologies are used to improve processes. Then, Six Sigma tools are applied to reduce deviations and defects. Design for Six Sigma (DSS) and Design for Lean Six Sigma (DLSS) are methodologies used to design (or re-design) products and processes from scratch using Six Sigma or a combination of Six Sigma and Lean tools. These methodologies focus on getting it right the first time rather than improving it later.
It is worthwhile to note that Six Sigma and Lean have been customized and specialized for many industries.