Is a nucleophile also a Lewis and Bronsted base

A Bronsted base is a species capable of accepting a proton like OH-, NH3. It may have a charge or be neutral. The concept is generally applicable for reaction in aqueous solution where protons decide acid-base.
Nucleophiles are substances which are rich in electrons and the concept is generally applied in nonaqueous medium e.g. H-(hydride ion) Cl-, NO2-, H2O , R-OH, amines, carbanions are all nucleophiles. This definition of nucleophile coincides with that of Lewis base.

No, it has a partial negative charge caused by a shifting of the electron cloud density that favors reaction with the positive charge of another atom. The Lewis and Bronsted base has a defined electron for sharing. For example: -OH