Great response.

If you know, or should reasonable know that a tree is dead or dying (both of which you have admitted too), you would be found liable if the neighbor can prove it. If a healthy tree falls due to wind, it would be considered an act of nature and you wouldn’t be responsible.

Tree falling.
 

A tree fell during a stormin Indiana. It caused $7,000 damages. Our insurance had to pay, not the neighbor whose tree it was. I don't know FL law.

I could be wrong, I’m not an attorney, but if your neighbors dock is in the lake and your tree falls on it, I doubt there would be any recourse to you since the dock was not on your neighbors property. Your neighbors land does not extend beyond the high water mark of the lake. In addition, if the tree is noticeably at risk of falling in the direction of the dock, it should be a reasonable expectation that your neighbor should assume responsibility for putting their dock in harms way. All that being said, talk with the neighbor and try to find a mutually agreeable solution to the problem. It’s always best to prevent a problem rather than wind up lining the pockets of a couple attorneys after the fact.

I'm from Virginia. There, if you didn't know the tree was an issue and it fell, the neighbor's insurance would be responsible. If you knew it was a problem and it fell, you would morally be responsible. If your neighbor and you both knew there was a problem and you didn't do something about it, you would be responsible.