afroakuma's Planar Questions Thread! (You ask, I'll answer)

[Larkas]

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She killed his Avatar, which removed his foothold from Sigil. After which, he was ejected from the plane like all other Divine beings who try to set foot there.

Also, why did the Lady kill Aoskar and/or why did he try to enter Sigil?

IIRC, Aoskar was a god of Portals. It made plenty of sense for him to try and control the city. She killed him basically because he got on her nerves and tried to ignore the city rules.