For the item to be considered 100% gold efficient, the passive and active would need to have a combined gold value of 800g.
During the active, Sword of the Divine becomes 372.1% gold efficient then drops to 0% gold efficiency once the active is done
If the Active Is used whenever it is up and assuming that no kills are made, the average gold effeciency ranges from 7.44% (when attack speed is capped) to 18.6% (when the active is in effect for the full 3 seconds).
While JudgmentGaren will benefit from the 100% critical strike chance, each critical strike will not count toward the 3-critical-strike limit.
On the contrary, Parrrley will consume one of the strikes. As such, the critical strike counter is consumed on-hit rather than on-critical-strike.
Even though you cannot critically strike structures, it won't allow you to retain the bonus attack speed for the full duration, it will go off after the third strike.
Lucian's ultimate, The Culling, will ignore the bonus attack speed from Sword of the Divine. This is a special case, "to prevent abuse", and is intended by Riot. It, along with Silver BoltsVayne and Runaan's Hurricane, are the only champion-oriented special cases coded into items.