This is a curiosity that the FAQ leaves woefully unclear.
FAQ §1.42 "Additional attacks by an enemy":
When an enemy makes an additional attack, discard all of its previously dealt shadow cards before dealing it a new shadow card.
Note that this does not actually say to deal the enemy a shadow card for the new attack, only that you should discard any existing ones before the enemy makes its second attack. Nowhere else in the FAQ or core rulebook does it even mention multiple attacks by one enemy, much less any potential shadow cards dealt to them.
Also note that within the normal framework of the game, dealing shadow cards to engaged enemies is done only at the beginning of the combat phase (as per the core rulebook, and barring any specific card effects which instruct one to deal shadow cards).
Unfortunately, the card pool itself doesn't give any consideration or set any precedence for a specific answer.
Lord Alcaron specifically tells you to deal a new shadow card:
Forced: When Lord Alcaron is dealt a shadow card with no shadow effect, he makes an additional attack after this one (deal and resolve another shadow card).
But Old Orc-eyes (from Murder at the Prancing Pony) specifically tells you to not deal a new shadow card:
Forced: After an attack resolves in which Old Orc-eyes was dealt a shadow card with no shadow effect, he makes an additional attack against you. Do not deal Old Orc-eyes a shadow cad for this attack.
No other card in the existing card pool which contain the possibility for additional attacks (for example, Smaug the Magnificent, Angmar Captain, or the shadow effect of Lawless Ruffian, which spawned this question) specify either way.
EDIT:
FAQ §1.26 "Enemy attacks outside of the combat phase" could be seen as setting a precedence for all attacks being dealt a shadow card, but again, nothing is specific about "additional attack" text.
Edited by caelenvasius