In the following molecules:
BF3, BCl3, BBr3, BI3 I , II , III , IV
The correct order of Lewis acidic strength will be:
IV > III > II > I
These are all Lewis acids, and the halogen atoms - with their lone pairs - can partake in back-bonding into the pure, unhybridized 2p-orbital or the central Boron atom in each compound. As the size of halogen atom increases, effective overlapping of orbitals (via back-bonding) decreases. This means that the extent of back-bonding is the least in BI3 and that will be the most reluctant to accept an e–pair among the given boron trihalides.