A public records request sounds plausible. This would explain why the PDF looks different from the other PDFs published on CARB's website.
This PDF of Lotus Emira approval is all images except for one small bit: the California Public Records Act stamp at the bottom right:
View attachment 37873
Searching on line for other documents issued by CARB according to CPRA requests, while not exact matching in format, the location and overall format of this CARB CPRA stamp is very similar. It looks like the person made the request on 1/5/2024 and has either been following up periodically, or this CARB bureaucrat put it on his "to do" list and followed up on his own and sent this approval PDF as soon as it became available.
I also would not put it past it that some Lotus/Emira enthusiast actually knows someone or works at CARB and knows about the CPRA mechanism and was able to get it released earlier than the batch EO publication.
I'm going to go with 95% confidence that this is real.