Perhaps my input may be more theoretical than practical via experience, but I believe that any OEM type of air-filter box is going to have it’s limitations due to it’s design. The surface area - laid flat - of the filter is probably adequate, but the way that the cartridge is encompassed provides some restriction. The proof of that is Innocenti re-designed the later ‘boxes & Servetta did away with that type completely. Why would either company have spent money/resources unless it was necessary, though in Servetta’s case, it may have been due to supply problems
However, I believe that a good, clean, cold, plentiful air supply is necessary for any engine that has the potential to provide a good increase in performance, not only for a good, complete burn but also to augment the top end cooling.
I reason that the frame hole being 50 mm shouldn’t be a problem, but the OEM filtration system is restrictive. That’s why I believe that adding holes to the box can increase air flow but in so doing introduces warm air. It would never be my choice
Gradually we are all evolving with our machines & an evolution of the air filter system is long overdue, with the potential to fit on machines with intake either side & with the OEM battery & tray location. Of course - & I have considered this - the OEM air scoop, even as fitted to the later machines, may then be restrictive, but it shouldn’t prove too difficult to replicate a slightly larger scoop that looks ‘factory’ especially nowadays with 3D printing.
Getting back to the OP, then it seems fairly obvious that an increase in the supply of filtered air will necessitate up-jetting & on a Lambretta large frame machine utilising SH carburettors, that is not difficult to do. Personally, if I were to fit a better flowing cartridge type filter, I’d be disappointed if I
didn’t have to increase the main jet size to compensate……
