Its worth pointing out how Supersymmetry almost solves the problem and how it elucidates the nature of the issue.
Assume that <P> appearing above, was for some reason identically zero, then indeed lambda effective would just be a constant of integration and everyone would be happy. No rhyme or reason why its small or big, or whatever. Who cares, its just a number that experiment happened to find. You could invoke the anthropic principle trivially if you really wanted too at that point and no one would mind.
And indeed, in exact rigid supersymmetry it was noted long ago that fermion loops exactly cancel boson loops and the net vacuum contribution is zero (at least perturbatively).
The problem is, exact supersymmetry is not the way the world works, and it must be broken. When you break rigid supersymmetry in this framework you induce terms that necessarily set <p> != 0 (and if you include gravity and make the susy local, the superpotential and the kahler potential will not in general exactly cancel!) and you are back to worrying about how weird it is for physical cancellations to take place of that magnitude (although now, the problem is cut in two on a log scale and may also be sensitive to exactly where the supersymmetry breaking scale is set)