Due to it’s broader definition it allows Bronsted-Lowry Acids and Bases to come under as a sub-category.
Lewis Acid
→ Acids accept electron-pairs. Any electron-deficient atom can act as a Lewis Acid. Many compounds from group-IIA only have a sextet of electrons, and thus can act as Lewis Acids and expand to an octet. Atoms with vacant orbitals can also act as Lewis Acids.
Lewis Base
→ Bases donate electron-pairs.