The correct order of Lewis acid strength of boron trihalides is

In $\mathrm{BF}{}_3$ the $2p\pi$-$2p\pi$ back-bonding from F to B is the most effective (similar orbital sizes), which reduces the electron deficiency of boron most. This back-bonding weakens down the series as the halogen $p$ orbital becomes larger and diffuse. Hence acid strength increases $\mathrm{BF}{}_3<\mathrm{BCl}{}_3<\mathrm{BBr}{}_3<\mathrm{BI}{}_3$.