What's their relationship besides former lovers?

Thanatos is constantly trying to impress her, but she really doesn't give a damn about him

Crap, I meant Thanos no Thanatos , stupid spell check..........

She does care for Thanos, as shown in his series, Annihilation and the Thanos Imperative, but it's complicated.

Dude she's hot

At one point Death considered Thanos her superior when all he wanted to be was her equal. Thanos was also heart broken when she wouldn't even address him directally. Thanos then decided to form the infinity gauntlet and wipe out half the universe.

Didn't Death ban Thanos from her realm by making him immortal?

yea she did ban him and he's still bitter over it

There's some extremely convoluted relationship that is kinda like necrophilia.

^^ No it's not. She's the personification of death not dead herself...