It happens when you're ready to put all of your cards on the table, right before you
attack the Cerberus base head-on in search of the Prothean V.I.
You'll have the typical "Are you sure?" dialogue (with Admiral Hackett) once you go to begin this mission.
As CaulynDarr notes, the actual Paramour achievement itself is awarded earlier in the game following the
Cerberus attack on the Citadel
While I'm unsure of the specifics for all available romance options, a "successful" relationship with Liara in my playthrough revolved around three key conversation events:
- Liara asks about your other romance option in Mass Effect 2, if you had one
- Liara asks you to come to the Presidium Commons on the Citadel (Paramour achievement is awarded at this point)
- Liara visits you in your cabin prior to the final mission