Neither Phil Plait nor the ESO website have looked at the other side of the coin. Maybe it's not that having planets destroys lithium, but that NOT having them or LOSING them, adds or stirs-up lithium.

One scenario for lithium abundance in stars is planetary capture. The theory goes that most stars destroy lithium, so an old star with higher lithium values "must" have relatively recently captured a large amount of the stuff, perhaps by swallowing one of its own planets, which was effectively a "lithium bank".

of course, we would then expect more recent captures to show higher lithium anomalies, and in any case, the amount of Lithium offered by a single planet (or even a whole planetary system) would only be a tiny percentage of the mass of the primary star - even for the case of a giant Jovian and a small L or M class star.

I think we need more ideas on this one...