You say the water is pooling at the lip and spilling out, and your comment says that the "lip" is in the middle of the wide part.
So here's what's happening --
What you're calling the lip is the two flanges that join the upper part to the lower part of the fan housing. Those flanges are joined either by solvent welding or ultrasonic welding. The joint is supposed to be air tight and waterproof, but yours has an imperfect seal. If you put some soapy water on the lip, you'll see bubbles. That's where it's leaking.
When rain falls into the vent pipe and into the fan -- or when moist, relatively warm air from under your house condenses inside the fan during cold weather -- the spinning fan catches the water and flings it radially outward, directly at the "lip", and drives the water through the space between the flanges that is supposed to be perfectly sealed. There's your water leak.
If this fan is still under warranty, the manufacturer should replace it because their airtight waterproof seal is leaking.
If it's no longer under warranty and you want to repair it, make sure the lip is clean and dry, roughen the outside circumference of the lip with some coarse sandpaper, mix up some epoxy and coat the lip with it to plug up the crack between the upper and lower flanges. Best to do this with the fan turned off, or the crack may blow epoxy bubbles and fail to seal. If you use 5-minute epoxy, leave the fan off for an hour till it's good and firm. It won't leak any more.
Leaving the fan off for just an hour won't make any measurable difference in radon infiltration.