The question still remains: is it absolutely necessary?
Is it a question that can be demonstrated in a realistic experiment?
Apparently yes. All you have to do is
find some superfluid helium.
Increasing viscosity descreases lift. Hm.. Do you meant, beyond certain point, or always?
Beyond the trace of viscosity (present in every fluid that isn't a superfluid like helium 3) that is necessary for lift, lift generally decreases the more viscous the fluid, with all else equal. I'll see if I can dig up a graph.