Why is F a Lewis base?
First of all, what is a Lewis base or acid?
The term Lewis acid refers to a definition of acid published by Gilbert N. Lewis in 1923.
An acid substance is one which can employ an electron lone pair from another molecule in completing the stable group of one of its own atoms. The modern-day definition of Lewis acid, as given by IUPAC is a molecular entity that is an electron-pair acceptor and therefore able to react with a Lewis base to form a Lewis adduct.
A Lewis base, then, is any species that donates a pair of electrons to a Lewis acid to form a Lewis adduct. For example, OH− and NH3 are Lewis bases, because they can donate a lone pair of electrons.
You can now imagine why F is a Lewis base. It hase 7 electrons in valence shell.