In the BCl3, due to small size of B3+, BCl3 is covalent. Still, the octet of B remains incomplete. In NH3, N has a lone pair of electrons. Hence, N shares lone pair of electron with B to complete the octet. Hence, BCl3 acts as Lewis acid and NH3 as Lewis bases.
AlCl3 forms dimer by completing octet of Al involving p-orbitals to accept electron pair from chlorine.
