Rope

You reach out for it and tell him up front:

Lily: Well done, my sultan! I heard you like to be chocked a little, want to get some today?

Sultan: Yes, yes, do it! Then ride me, I can barely hold it any more!

You tie the rope around his neck, and pull it with all your strength... He tries to cry out for his man but he can't get any sound through his throat... Soon he stops moving and you look at the mess you have made... The deed is done... Your captor and the killer of your husband is done for... What now...? His guards will still cut you to pieces if you attempt to walk out of the room... Yet, there is no other way out. You walk to the door but hesitate to open it... But go through with it anyway after a deep breath... The guards look at you. There are four of them and Erik. One of them looks into the room and sees the dead body! He grabs his sword, trying to kill you, but Erik stabs him in the back with a knife and impales an other with his sword... The two guards taken by surprise, fail to stop Erik from cutting them down. He looks at you and smiles.

Erik: You have done it my lady... The damned sultan is finally dead! I wanted to do this myself, but you have found a faster way! We will talk later, we must get out of here!

You nod and tell him, if he takes you to the harem girls, you could get Fatima out too. He should simply tell anybody who asks about anything, that he is taking you two to the cells below to be gotten rid of. Sounds simple enough, yet it works... When nobody moves you three get out of the palace via a window and disappear into the city. When the soldiers realise what has happened, they are unable to find any of you.

Fatima (catching her breath after you all ran a lot): Lily...huh..... I don't know...huh..how to... huh... thank you... huh... for saving me today!

Lily (evenly tired): Don't even... huh... mention it! Do you want to... huh... come and... huh... live on my estate?

Fatima: I have never... huh... been more determined to... huh... accept an offer!

Erik (without breaking a sweat): Now, that it is settled, time to find a way home...

Find a way home with a bodyguard, no coins and no clothes for either of you girls, without raising suspicion... At least you weren't slaves any more, but you still looked like ones, running on the streets with no clothes...