One form of the LC&P sum rule is
2 λ + g2/4 + (g2 + g'2)/4 + yt2/2 ~ 1
... based on their equation 2, and neglecting yukawa couplings for fermions other than the top quark.
As they remark (but I didn't notice until Andrew pointed it out), the contributions from bosons and fermions are almost equal. So we can also say that
2 λ + g2/2 + g'2/4 ~ yt2/2 ~ 1/2
The "fermionic part" of this makes sense, if we recall that yt ~ 1. But the bosonic part
2 λ + g2/2 + g'2/4 ~ 1/2
... just considered by itself, seems to be very notable new numerology, connecting electromagnetic and weak couplings with the Higgs self-coupling λ.
edit: Actually, if I think about it for a moment, I remember that g is small and g' (the weak coupling) is even smaller. So the bosonic part reduces to
2 λ ~ 1/2
i.e. λ ~ 1/4. I noted almost a year ago that this is implied by the fact that the Higgs VEV / electroweak scale is approximately twice the Higgs boson mass.
edit #2: Study of the literature (e.g. PDG 2013 Higgs review) makes it clear that
λ ~ 1/8
is closer to the truth. Apparently there are some factors of √2 that I missed. But now I don't understand why LC&P works.
(Or are we just dealing with different conventions? Remedial study of Higgs-sector basics is in order...)