Theoretically, it is the way he does in this game. The only difference is the style, and the fact that Sonic 2k6/Colors/Genearations&Unleashed had the most free running bits throughout most of their games. Examples like: running long distances on walls, doing tricks on ground or airborne (or even underwater e.g. Sonic Rush/Rush Adventure), jumping from wall to wall. These can be considered extreme free running.
All that Sonic Lost Worlds has done is dumb Sonic down.