So based on what I've read, this is basically the relationship status of Sloth to each of the other members so far.

Sloth to Envy: While she doesn't think of him as a slave, she does find herself taking advantage of his severe loyalty, usually having him either give her foot massages or other such activities while she's either working on relaxing.

Sloth to Greed: Sloth views Greed as an asset and protege of sorts. She often finds herself using Greed's extensive druggie network he's established with his sales to get whatever information she deems is necessary, while also being the one to teach Greed how to actually fight and other gang related things...That is when she's not sleeping, working, or having Envy pamper her. When it comes to his flirty nature, she didn't mind it, in fact she found it somewhat flattering, but she never showed that she enjoyed it to Greed, at least not in front of the others.

Sloth to Wrath: Sloth has always viewed Wrath as two things, a superficial pity case hiding a nuclear bomb. She was fully aware of his capabilities to explode, and whenever he was around she felt something waiting underneath his "non-threatening" exterior, and whenever this bomb would explode, she would make sure that she was not in it's blast radius and that all her enemies were.

Sloth to Gluttony: She doesn't think that Gluttony is a threat, but that's as far as her read on him has "guaranteed." She can't make heads or tails of why he would exactly fund them and assist them, but hell having access to such a large fund when the gang was still fairly new and small was definitely a plus, so as long as she knew that he was on their side, she was fine with him.

Sloth to Pride: Sloth doesn't "like" having Pride around, but she believes he's the best fit for the role in terms of personality and ability. Overall, terrible guy but he's useful to her, so she's willing to use him.