I’d bet your bet is a safe bet. Gotta believe Lull probably has a proprietary spec their pickups are made to along with a no compete clause for the manufacturer. That doesn’t mean you can’t get very very close to the Lull sound, but when all is said and done it probably won’t be an exact match. At least that’s my gut feel, no data to back that up on.
I have a lot of different purchased Thunderbirds with a lot of different pickups. I also have a tendency towards mad scientist type creations - mixing and matching pickups, control and cap variations, active and passive options, hardware and body and neck variations in my personal builds. My current Thunderbird pickup line-up includes:
Gibson stock 2021 NR cans
Gibson reissue cans
Gibson Bicentennial cans
Gibson 1991 cans
Gibson 2012 plastic cap
Gibson 2015 DeCola plastic cap exposed poles
Lull 4 string cans
Lull 5 string cans
Epiphone VP cans
Epiphone ‘64 reissue cans
Epiphone Goth plastic caps
Epiphone CSLE Les Paul rail cans
ChinaBucker (EY) cans
Greco 1975 cans
Greco 1990 cans
EMG Humbucker plastic cap
Bartolini Humbucker plastic cap
Burny plastic cap
Nordstrand Zen exposed rail plastic caps
Dingwall split coil plastic cap soapbars
Sammick cans
Altec plastic cans
Fender wide range humbucker exposed pole cans
I can record and compare any of those you want but to be honest they’re all in different basses, most have different strings, some are active, some have different cap or pot values, and pickup locations vary widely. All those things combined will unfortunately result in an apples to oranges comparison, but I can note the physical differences so you could directionally account for tone differences in the recording if that helps.