"Lord" is a title unique to Avalon, reserved for knights.
To be called "Lord" means to become a knight knighted by the Queen.
Edward's extraordinary skill had already reached the threshold of the Arbitration Hall, but he had previously declined an invitation from the Arbitration Hall due to his foster father's opinion.
As a member of the Moriarty Family, it's unlikely for him to enter the Round Table Hall. The armor inherited by the Moriarty Family is the armor left by Mordred, the founder, and this set of armor was worn by Old James.
The Queen could not possibly knight the other members of a founding family, essentially a split family. Therefore, Edward could not simply enter the Round Table Hall through knighting like a commoner.
To circumvent this rule, one must obtain armor that is not passed down to descendants in their personal capacity.
And this type of armor is usually the ministerial armor, which is received upon taking office and relinquished after stepping down.
