Generally speaking, lies by omission are considered a form of lying, yes.
But, swinging this back to 'Rigid Personal Code' if a person who declared to themselves that they will never tell a lie really are saying that they will never tell an overt lie.... Well, they are leaving themselves all sorts of wiggle room, aren't they? 'Technical Truth' being one of the lower rungs and 'From a Certain Point of View' being the highest rung of the ladder.