Why does phosphorus tribromide act as a Lewis acid (electron acceptor)?
The why of a mechanism is always the best approach.  

The reasons for this attack are:  


$\ce{P}$ can expand its octet due to presence of vacant $d$-orbitals.  
The $\ce{P-Br}$ bond is polar due to the electronegativity difference between the atoms and hence P develops partial positive charge favouring a nucleophilic attack on it.    
Looking at the molecule as a whole, $\ce{Br}$ is a good leaving group so $\ce{P}$ doesn't mind a nucleophilic attack on it by the lone pair of oxygen.  
"Nature loves stability" and  $\ce{P-O}$ bond is stronger than $\ce{P-Br}$ so that might be the driving force for this reaction mechanism.