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A triggered ability is a type of ongoing ability that is delayed until a specific scenario or game action takes place. When the given situation occurs, a triggered ability activates, and can be tied to either an instant or ongoing effect....While triggered abilities are triggered by a condition or situation happening, they may not insert themselves between other abilities to resolve. Instead, they are pending until all other abilities resolve, and then the triggered event may activate.
The phrase “interrupt the battle” includes interrupting the following:● all active ongoing abilities● abilities that are defeating one of the characters you control in battle● the last card played in current battle if it was played by your opponent.Interrupt the battle only includes such abilities if they were activated on cards in the current battle.
If there are pending abilities when an end the battle ability occurs, the pending abilities never take effect.
With that in mind, a ML that is in battle is interrupted by 2KH; all triggers are 'ongoing' effects, and since it was played in battle, it would be interrupted. While interrupted, it is temporarily undone, and thus cannot be active. Regardless of any other effects, you cannot activate his ability based on the draw of 2KH or anything else that occurs during the interruption. Those things happened when it wasn't active, and before it later reactivates (as per the definition of interrupt); it cannot trigger off of any draws or searches happening in-between.
Quote from: REG 3.0.0 Interrupt > Special ConditionsThe phrase “interrupt the battle” includes interrupting the following:● all active ongoing abilities● abilities that are defeating one of the characters you control in battle● the last card played in current battle if it was played by your opponent.Interrupt the battle only includes such abilities if they were activated on cards in the current battle.