Chemical species that possess empty orbitals and can accept electrons into them are said to be Lewis acids.
Chlorine's electronic configuration is . Thus, it has 7 electrons in its valence shell and its octet is incomplete due to which it is not very stable. It needs 1 more electron to complete its octet and become stable. Therefore, Chlorine is highly electronegative (3.16 on the Pauling scale).
Barium's electronic configuration is . Its valence orbital is fully filled due to which it is relatively more stable and less electronegative than Chlorine (its electronegativity is 0.89 on the Pauling scale).
In Barium chloride (), two Chlorine atoms accept one s-orbital electron each from barium. In doing so, both chlorine atoms completely fill their valence p-orbital (completing their octet) and attain a stable electronic configuration. The barium atom loses both of its s-electrons and attains the stable electronic configuration of . Neither of the atoms has an empty orbital left to accept electrons. Thus, barium chloride cannot behave as a Lewis acid.
Barium chloride is not a Lewis acid because it has no empty orbitals to accept electrons.