Planet lifting typically involves building refineries around gas giants and lifting enough material so that the planet is transformed. This would happen once all the useful energy of a gas giant is removed.
At the center of most gas giants is a rocky core trapped inside a thick and hazy atmosphere. By planet-lifting, you could remove a gas giant's atmosphere and outer layers and be left with a rocky, Earth-like planet. This modification of the planet's physical properties is called planetary husbandry, analogous to stellar husbandry in star lifting.
Thereafter, by using fusion candles, the planet could be moved to its parent star's habitable zone. A gas giant propelled using a fusion candle system will bring its moons and anything else in orbit with it. Finally, the process of terraforming could begin.