Lewis acid is defined as the substance (atom, ion or molecule) which is capable of accepting a pair of electrons. In other words, a Lewis acid is an electron pair acceptor.

⇒All cations are Lewis acids because they have a tendency to accept the pair of electrons.

⇒Molecules having a central atom with incomplete octet

Hence, H⁺ and being cations are Lewis acids and in BF_3,the boron is electron deficient and has an empty orbital, so it can accept a pair of electrons, making it a Lewis acid.