Well, Eva already introduced the rent hike. Seymour is buying property, so the suggestion might be that his purchases are driving up land values in the city, which is the cause of increased rent, even if indirectly.
So I could see Lena moving depending on her relationship to Seymour, as opposed to Stan and Louise, though they of course could still be secondary causes.
If Lena is on the Seymour route, would it not be a sensible development that Seymour offer her a place to live? Similar to how Ash can have the option to move in with Jess in GGGB depending on her status.
Alternatively if Lena is not on the Seymour route he could force rent up to a point where Lena can no longer realistically live as centrally as Stan's apartment seems to be, forcing her to have to consider moving away.
If this was the structure then Lena moving out would be a matter of when rather than if. Of course on the Stan route it's possible she could stay in the current apartment if Stan's willing to pay the rent, he does have full time employment. Ash could choose to stay in her childhood home in GGGB too