First thing's first: Lincoln's departure doesn't mean that Rick will necessarily be killed off. There are plenty of other ways to write the series star out of the show.
For the past three seasons, the Alexandria settlement has been the main focus of the show, with Rick, Michonne, and Carl building a family there.
But with Negan burning Alexandria to the ground, it's likely that the survivors will move along to one of the other settlements where they can reside permanently. Additionally, the Season 8 finale seemed to suggest that the Hilltop is going to be our survivors base of operations moving forward, so perhaps Rick will opt to stay in Alexandria on his own so that he can rebuild what Negan destroyed?
Alexandria was arguably where Rick experienced the most happiness, so this would make sense. Moreover, due to the destruction and devastation the settlement suffered, none of the other series regulars will be returning there, which means we would never actually need to see Rick. It would be a great way to leave the door open for Lincoln to return at a late stage.