Brutus? (After all, he does quote from 'Julius Caesar' when he sees Mrs. Cox in handcuffs.)
Cassius? (Because he's often mentioned in the same breath as Brutus in said play...)
Of course, I could also see him name the dog after a great king of old. (And, yes, I see the dog as male - I can't imagine Lex preferring a female dog over a male one.)
I think the perfect name is Midas. (The king who turned everything he touched to gold...)
