I believe there is a general misunderstanding about how lightning rods
work. It's not clear whether the original poster understood or not, so
I'll just chime in anyway.

A static charge builds up in the air during a lightning storm. It
originates in the clouds, but induces an electric field through the
atmosphere. When the voltage between two points (two clouds, cloud and
ground, or cloud and building, animal, person, tree, etc.) builds up to
the breakdown voltage of air (on the order of 10,000 volts per inch
distance) then an arc or spark (lighning) jumps between the two.

To prevent such arcing, you want to dissipate the electric field in the
vicinity of your building.

Now, what's not always understood is how an electric field induces an
opposite field in an object. I.e., if the cloud is negatively charged
(sorry - I don't recall which charge the cloud normally will have) then
it will induce a positive charge in the building.

The critical thing is that this positive charge will not be uniform
across the building. It will be greater on the roof, and will have the
greatest charge density at abrupt corners. What a lighting rod is is a
VERY abrupt corner.

When the thunderstorm passes into the area and starts inducing electric
charge on buildings, the charge density at the tip of the lighning rod
becomes so intense as to leak current. This, in turn, dissipates the
field. Exactly what we want to accomplish. (Thank you, Benjamin
Franklin!) At the voltages we're dealing with here, this would be true
whether or not the lighning rod were grounded. But the current to
(from?) the rod must travel through something, and if the reisitance of
what it must travel through is great, its voltage will rise to that of
the air, ending its effectiveness at dissipating the charge. Hence,
the rod must be grounded sufficiently to conduct whatever current it
must, or else it will end up attracting lightning.

Hope this helps.