Can Jason and Lucia's relationship change?
Yes. Players can shape them as lovers or primarily as partners.
Rockstar North says the relationship can deepen or weaken and can unlock or remove certain couple interactions.
The evidence
Explicitly stated by an identified primary source.
FamitsuFamitsu interview with Rockstar North co-head Rob NelsonEL PAÍSEL PAÍS visits Rockstar North for a GTA VI demonstrationRockstar GamesGrand Theft Auto VI official siteRead the full supporting guideWhat would change this answer?
A final relationship-system breakdown from Rockstar.