Rage says "Play when you activate a monster. The monster may attack twice during this activation (four times if it has Quick Shot)."

When a lieutenant activates, it may choose to run, which lets him move double his speed but prevents him from attacking.

Which takes precedence, the general rule for running or the specific override given by playing Rage?

From the GLoAQ :

"If the Overlord plays RAGE on a Lieutenant during a battle action, how many attacks does he receive - 3 or 4?
Two, actually. "Rage" reads: "Play when you activate a monster. That monster may attack twice during this activation (four times if it has Quick Shot)."
A lieutenant who has declared a Battle action may attack twice during his activation. "Rage" has no further effect - it is essentially granting the lieutenant an ability it already has. A much stronger play is to declare a Run action and then play "Rage," which would allow the lieutenant to move twice his speed and attack twice."

The clause on Run that says you cannot attack is almost certainly a mistake in the same vein as the original description for Battle saying that you cannot move; it actually means that a Run action does not grant you any attacks, not that it prevents you from making attacks that you're otherwise entitled to.

Personally, I think that the Rage card should originally have been written to grant a monster one extra attack, not to set its number of attacks to exactly two. (And I changed it to that effect in Enduring Evil.) But it is what it is.