Because Double Strike is a Reaction and not an Action, it must be used in response to Luke (or any other character unit) focusing to strike and could not be held until after the engagement. Here's the rules text for Reactions from pg 25:
Reaction abilities are clearly labelled by the word
“Reaction” followed by effect text. Reactions may only be
resolved after a specified triggering condition occurs.
Unlike interrupts, which resolve before the triggering
condition is completed (and may change the outcome of
the triggering condition), reactions are played after the
effects of the triggering condition have resolved.
The active player has the opportunity to resolve the
first reaction to a triggering condition, followed by his
opponent. In this way, players execute one reaction at a
time until both players consecutively pass. Resolve each
reaction completely before the next is executed.
A card’s reaction effect may only be resolved once per