(N/A) In $BCl_3$,Boron is attached to three chlorine atoms by covalent bonds,but the octet of Boron is incomplete. It requires two electrons to complete its octet.
Such electron-deficient molecules have a tendency to accept a pair of electrons to achieve a stable electronic configuration and thus behave as Lewis acids.
$BCl_3$ easily accepts a lone pair of electrons from ammonia $(NH_3)$ to form the adduct $BCl_3.NH_3$:
$H_3N: + BCl_3$ $\rightarrow H_3N$ $\rightarrow BCl_3$
$AlCl_3$ achieves stability by forming a dimer,$Al_2Cl_6$. In the dimer,each Aluminum atom is bonded to four chlorine atoms,two of which are bridging chlorine atoms. The structure is shown below:
(See the provided image for the $Al_2Cl_6$ dimer structure.)