re. proper title, well the drivers, the box and the brochure use some of this interchangeably [Lexicon Studiocore-32 system] so there is no correction to be made in my opinion. See manual '...The PC-90 module can only be mounted onto a Lexicon Studio Core-32 system card' - whole system is referred to as lexicon studio but the PCi card (you make this point), drivers as 'studio core-32'...
This chap posted up a theory of ops for the unit on a sourceforge project to enable usb that never got off the ground :
https://sourceforge.net/projects/lexiconstudio-i/Had i known about the above i would picked up a LDT-10T, which i saw going without a cable and worked out the connections (it is a bespoke AMP narrow cable). There is a service manual for the Core -2 but not for the Core-32.
as for hoping for a G4 update
well the item was hastily removed and it seems G4 drivers were promised but they don't seem to be on the FTP. I have noticed there is a beta for faster ASIO performance and Lexicon were not fastidious about keeping documentation or drivers for these cards and so there is a chance a user may have a beta G4 release of the driver.
Looking at the Theory of OPs there is no h/w reason for the card not to work on a G4 (cf. AMCC bus master chips on Audiomedia IIs until rev QC).
If i can't get it to work in a G4 i may just off-load as whilst it works on Windows 98 that is not a happy environment for audio.