Hello!
Just to let you know. The reason why your KLE 500 did not run well (I guess that's the situation, as you seem sure it's running lean (which is most likely the case)), is most likely due to a lean air-fuel-ratio, but that's not all. Carbs in general must retain the needed pressure difference between the venturi and the float for fuel to pass through the main jet, which is why a bigger main jet is usually needed when modifying the intake (though this applies to most carburetors), but the main difference is that the slide will have trouble rising without an airbox, which is why POD-filters (or not airbox at all) do not work well at all with CV-carbs.
OK, so how do you actually fit the airbox to the carburetors? There is not much space to play with, though this is usually not a problem.
I usually use a flat screwdriver to attach the ducts properly, connecting the airbox to the carbs (though be careful not to damage the ducts (rubber pieces)). Put a small amount of force to these rubber pieces away from the carbs, increasing the size between the ducts and the carbs, and then try to seat the airbox properly.
Make sure the springs are "slided away" while attaching the carbs to the airbox. When that is done, it's time to seat the springs in their correct position on the ducts.
There's not much more into it, as far as I can see (have never seen this as a problem at all, so might miss something).
If there's something else, please do not hesitate to ask. I might missunderstand the whole situation
edit: Quick question. Is the airbox from the same generation as your bike? Why I'm asking is due to the fact that KLEs pre 96 (96 included, if I am not incorrect), have a bigger snorkel than the newer ones. If you have a small snorkel on that airbox (see the carb tuning thread for picture references), the bike will not run well without modifications (if you have a KLE from 95).
Regards,
Mollrik