Lucid Air today published the results of their testing: 500 miles range with 113 kWh battery. That translates to 4.5 miles per kWh, which is 0.5 miles more per kWh than Tesla with their Model S. The testing was done by the German automotive engineering company FEV, which has a good reputation in the automotive industry.
Which battery system is Lucid using for their Air? They planned on using cylindrical cell type 21700 from LG Chem, the same size as Rivian is using for their RS1 and RT1. With this kind of efficiency boost, it is very likely that they have further improved or even used a new battery pack design. We are still waiting for more information on the thermal management system.