I remember Lucid talking about end cooling battery cells long before Tesla started talking about it. It could be a technique learned from the Atieva racing that they carried over to Lucid and Tesla picked up on.
I'm pretty sure that Lucid's battery pack engineering and power management are at the cutting edge. However, I think that is completely in-house technology and partially independent of the cells themselves. Reports are that the Dream Edition will use cells from Samsung, and other versions of the Air will use cells from LG Chem. In discussing its collaboration with each manufacturer, Lucid suggested the Samsung joint venture was more about cell chemistry while the work with LG Chem was more about optimizing the battery pack to take best advantage of the cell chemistry.
This is from a December 6, 2016 release from Lucid:
"Samsung SDI and Lucid have collaborated to develop next-generation cylindrical cells that are able to exceed current performance benchmarks in areas such as energy density, power, calendar life and safety. Significantly,
this jointly developed cell [my emphasis] achieves breakthrough tolerance to repeated fast charging."
The February 24, 2020 announcement of the LG Chem agreement seemed to suggest that the collaboration was now more about using LG cells as they are but engineering the pack to optimize their characteristics:
"Lucid selects the best battery cell for each version of the Lucid Air based on data collected during comprehensive and proprietary performance tests, with the cells from LG Chem selected because they provide the ideal level of efficiency for standard versions of the Lucid Air. In conjunction with its proprietary battery architecture and flexible manufacturing technique, Lucid will optimize the LG Chem cells to meet or exceed all target goals for range, energy density, recharge/discharge rates, and more. In this way, Lucid will leverage the specific cell chemistry of LG Chem’s batteries to develop the most compact, yet energy dense, battery pack form possible."
These two announcements were over three years apart. Perhaps some of what came out of the 2016 collaboration relating to cell chemistry advancements had become more widespread by 2020?
You have written earlier that you think the battery packs may be different between the Dream and the Grand Touring. I have tended to think not. But as I ponder what I just wrote here, I'm thinking you are right. The packs for the Dream and the GT use cells from different companies. The chemistries may differ enough to explain some of what you're seeing in the energy consumption numbers
vs. range numbers.