Does the Relentless Pursuit move to base after conquering use the ready of the unit?

No, the move to your base granted by Relentless Pursuit does not use or consume the unit's "ready" ability.

According to RiftJudge FAQ #8229, when a unit has both a printed "ready" ability (like Lucian's) and the "When I conquer, you may move me to my base" ability granted by Relentless Pursuit, they are separate triggered abilities that occur simultaneously upon conquest.

Key Details:

• Independent Triggers: The move to base and the unit's ready ability are distinct triggers. You can choose the order in which to resolve them.
• No Cost: Moving via the effect of Relentless Pursuit is not a "Standard Move," so it does not require the unit to exhaust, nor does it consume any "ready" status or ability.
• Simultaneous Resolution: As noted in the FAQ, if you have multiple "When I conquer" abilities, you may order them however you want. You can resolve the move to base first, then resolve the ready ability, or vice versa.

In summary, the move to base is a separate effect granted by the spell and does not interfere with the unit's own ready ability.