While Garen'sJudgment 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 Vayne'sSilver Bolts and Runaan's Hurricane, are the only champion-oriented special cases coded into items.
The original Sword of the Divine was removed in patch V22.214.171.124 due to dodge being removed from the game.