Opinions will differ on this, but it wouldn't be my cup of tea for a few reasons.
First, I might not understand what you mean, but there are already several options for getting on the Internet with system 6 and system 7 Macs. Some of them work with flavours of MacWorks on the Lisa already. I guess a parallel port transceiver would be faster, but how much does this add to existing options? Probably the Internet experience on a Mac-ified Lisa isn't really affected as much by the connection speed as it is by the other aspects of the computer (small memory, processor speed).
Second, let's say you're talking about something different --- FujiNet isn't just Internet, it's its own system I suppose. If you have a classic Mac with FujiNet and a Lisa running System 6 or 7 with FujiNet... why use the Lisa instead of the Mac SE? The SE will be a bit more compatible with more Mac software, it will be a bit faster, it'll probably have more RAM, it will have square pixels (most Lisas won't) and a screen whose size matches the screens the Mac software developers were familiar with. I think you will have a nicer time with the SE.
Third, a FujiNet driver for the Office System would probably inspire some cool new software developments for the platform. I think we're about to enter an exciting time for 7/7: people are starting to take away interesting findings from the source code release and starting to gain experience with building complicated apps; LisaEm development is continuing (imagine emulated FujiNet?); and some folks are experimenting with AI-assisted coding (which isn't for everyone and doesn't have to be!). One thing though is that there really isn't much of a "target" to shoot for --- if we can make apps, what would we make now? The chance to "open the Office System up to the world" in the context of a networking system tailor-made for retrocomputing: that has a huge novelty factor, and I think it would build a lot of excitement!
That's why I would go for the Office System myself, but it also reflects my interests: I've always been more interested in the Office System and the Workshop (and maybe the Unixes) than I have been in MacWorks. I'd be curious to hear other takes!