How to identify the most stable Lewis adduct of boron trichloride?
You have to consider also the inherent strength of the covalent bond.  A strong covalent bond can entice an electronegative atom to accept some positive charge or give up some negative charge.

Roughly speaking, hydrogen and period 2 nonmetals form much stronger bonds among one another than with other elements, and this tends to override the electronegativity difference.  For instance, fluorine is much more electronegative than chlorine, but fluorine bonds so much more strongly with hydrogen that hydrofluoric acid is only a weak acid in water whereas hydrochloric acid is strong.  Note that the dissociation of hydrogen chloride in water creates hydrogen-oxygen covalent bonds.

Here, boron binds especially strongly with the period 2 nonmetals nitrogen and oxygen.  So (a) and (c) have this advantage, and after that (c) wins between these two by electronegativity difference.