Does Lucian's Legend ability work when using a challenge to attack a unit?

No, Lucian's legend ability does not apply when using the spell Challenge to attack a unit, unless that unit is already engaged in combat.

Reasoning

According to the rules, the Assault keyword provides a +1 Might bonus specifically while the equipped unit is an "attacker." Rule 733.1.d defines being an "attacker" as a unit that has gained the Attacker designation during Combat.

Because Challenge is a spell effect rather than a combat showdown, a unit targeted by Challenge does not inherently gain the "Attacker" designation. Therefore, it does not satisfy the condition required to trigger the +1 Might bonus from the Assault keyword granted by Lucian's legend ability.

Summary of Interaction

• Challenge: This is a spell effect, not a combat showdown.
• Attacker Designation: A unit typically gains the "Attacker" designation only when it moves to a battlefield and triggers combat.
• Result: Since the unit is not an "attacker" during the resolution of Challenge, the +1 Might bonus from the equipment's Assault keyword is generally not active.
• Nuance: If a unit is already attacking an occupied battlefield (in combat), it retains its Assault bonus during a Challenge played at that time.

Note: I could not fully verify this ruling against the retrieved rules.