All bronsted bases are also Lewis bases, but all Bronsted acids are not Lewis acid. explain.

According to Bronsted theory, an acid is a "proton donor" and a base is a "proton acceptor.
According to Lewis concept, an acid is acceptor of lone pairs of electron while base is a donor of lone pair of electrons.

So if a Bronsted base is acceptor of proton means it is donating its lone pair to the proton that is same aslewis base.
But to behave as Bronsted acid the species must contain proton, then only it will be proton donor. But any of the chemical species can be lewis acid if it accepts the lone pair of electron (here no role of proton). Example is AlCl3. AlCl3cannot donate proton hence not a Bronstedacid but it can accept lone pair of electrons hence it is lewis acid