This answer is speculative, so take it with a large grain of salt . . .
Lucid said in an interview that the 118-kWh battery pack has no buffers, as the Samsung batteries can tolerate full charging. No such statement has been made about the LG Chem batteries in the 112-kWh pack. In fact, Lucid's press release announcing the LG Chem deal notably omitted mention of tolerance of full charing, whereas their earlier announcement about the Samsung deal made a specific point about it.
Is is possible that the 112-kWh pack has buffers that the 118-kWh pack doesn't, thereby making the real difference in usable capacity between the two packs greater than 5%?
On the other hand, if each model was tested using the same EPA protocols, that difference should have shown up in their respective range ratings.
I doubt if the difference in horsepower and performance would have made any difference in EPA ratings as the test methods would not call for anywhere near full power from either car. Unlike with ICE cars where bigger displacements and other means of creating power output exact a mileage penalty at all levels of output, EVs are almost the opposite. The larger a battery pack gets for range, the more power the motors can generate within their output capability. In a sense, the added power of an EV comes "for free" as a consequence of larger battery packs. Peter Rawlinson has talked about this on several occasions when explaining that the Lucid's power was less an engineering goal than a side effect of the main goals which were range and system efficiency.