After this mission is complete, his Loyalty Mission will unlock - when you reach the end of this mission, do not act impulsively and attempt to shoot Akksul.
Once the mission is complete, check your email and respond to Jaal's offer to meet his family.
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If you choose to affirm your relationship with Vetra at this point, you'll lock yourself out of all other romance options for the rest of the game.
Express your interest for Peebee right off the bat and she'll echo your interest. Keep flirting (and helping her with her side missions) until after visiting the vault on Aya. When you return to the Tempest talk to her in her room.
Examine the gift she's left you to view her final romance sequence.
Liam is a Crisis response specialist and one of the initial members of your Pathfinder team.