The order of Lewis acidity is
BI3>BBr3>BCl3>BF3
The electronic configuration of boron 1s22s22p1. Boron halide BX3 is electron deficient as it's octet is not satisfied. This makes it a Lewis acid.
In boron halides the dative pi bond (back bonding) occurs between p-orbital carrying lone pair of electrond of halogen atom and vacant p-orbital of central B- atom. With increase in size of Halogen stom this overlap decreases due to larger size of p- orbitals. This phenomenon makes boron halide more electron deficient with increase in size of Halogen atom. So the above noted trend of Lewis acid is found.