‘The Lost Cut’ is a general term used for the assembly cut created by John Jympson. It is about as rough as it comes.

What I think you’re describing is a later cut either scored by John Williams or screened for Lucas’ friends and the FOX executives. Watching some footage and pictures of Williams’ scoring does show that there a few effects shots which were revised before release and the presence of some tracks (‘Land of the Sand People’ on the original album) indicates that several scenes were still much longer when the scoring process began.

By all accounts the early Tattooine scenes were scrapped before the later stages of post-productions, and until evidence of otherwise comes to light I’m inclined to think those scenes were scrapped very early in post-production.

There is a lot of evidence that the search for Artoo was much longer, including the presence of a graphic for the Landspeeder readout in the Visual Dictionary and there being some high quality color screencaps available for the original 1998 Lost Cut article despite the same article claiming the cut itself to be black and white. The same goes for some other shots that are clearly screen captures; Luke and Han congratulating each other after the battle, Luke deciding to leave the restraining bolt off of Threepio, miscellaneous shots from the climax, etc. These are the kind of things that would be present in these later cuts; smaller trims that to some might not even be noticeable, perhaps even with post-production elements mixed in like ADR dialogue or some rudimentary sound mixing.