What is Lucian's best first item when he mainly wants to impose lane and objective tempo?

Lucian's best first item is the one that lets him punish his short windows immediately. If he wins the trade but cannot convert afterward, the choice is not aligned enough with the champion.

When should Mortal Reminder be rushed on Lucian instead of simply pushing standard burst?

You should move up Mortal Reminder when enemy frontline, armor, or sustain stop Lucian from keeping value after his first burst. If his good sequences end too quickly, that correction becomes a priority.

Stasis or Quicksilver on Lucian depending on whether he mainly has to survive dive or keep his dash clean?

Stasis is better if Lucian can take the trade but mainly risks dying on the return. Quicksilver is better if one specific crowd control effect stops him from using his dash properly and replaying a second sequence.

Lucian Wild Rift Best Build Guide (Patch 7.2a)

Lucian's standard build works because it reinforces what he does best: win short trades, quickly regain tempo, and convert that pressure before true late game. He is not looking for slow scaling. He wants immediate damage and enough continuity to replay several clean sequences.