The script has additional information that Gumb took over the house when it was supposed that Ms Lippman moved to Florida and died there two years previously.
Clarice is talking to one of Fredrica Bimmel's (the first victim) friends, Stacy..who tells her that Mrs. Lippman died.
She died. She went to Florida to
retire, like two years ago? She died
This line is omitted from the movie though...but there is dialogue in the movie which covers the same ground.
Clarice: I'm looking for Mrs. Lippman's family.
Gumb: No. The Lippmans don't live here anymore.
[Omitted]...Conversation about why Clarice is there and whether he knew Frederica
Gumb: Mrs. Lippman had a son. Maybe he could help you. I got his card in here someplace. Do you want to come in while I look for it?
Clarice: Did you take over this place after Mrs. Lippman died? Is that right?
Gumb: Yeah. I bought this house two years ago.
So it's apparent that there was nothing suspicious about Mrs. Lippman's disappearance (assuming it was in fact her in the tub, and we don't know that it is).
Everyone thought she'd gone to Florida to retire.