Why are boron trihalides called Lewis acids?

Boron trihalides ($B{X}_3$) are classified as Lewis acids because they possess an electron-deficient central boron atom that readily accepts an unshared pair of electrons from a donor molecule to form a covalent bond.12

In these trigonal planar molecules, the central boron atom is bonded to three halogen atoms, resulting in only six electrons in its outer shell. Because eight electrons are required to achieve a stable inert-gas configuration, the boron atom acts as an electron-pair acceptor when it encounters donor molecules—such as ethers, amines, phosphines, or halide ions—that possess lone pairs of electrons.12

Upon accepting an electron pair, the boron atom transitions from a three-coordinated, trigonal planar structure to a four-coordinated, tetrahedral structure, forming a stable donor-acceptor complex known as an adduct.2