Disguising herself as the little tramp/vamp among the Novices was Jordan's idea of a joke to get Lanfear to the Novice quarters and reach Egwene and Nynaeve unseen.

This is most likely a spur of the moment idea (from the character, not RJ....). Lanfear had spotted Else before (unsurprisingly, she must have found her amusing) and that day she noticed she wasn't around looking at the Warders and trainees, so she adopted her appearance to cross the grounds and reach the girls without attracting attention. As soon as she left, she took back her own appearance (that Egwene confused with a sister).

Lanfear probably had no idea that Else had been put out of the Tower weeks earlier and that's why she wasn't around. She obviously had no idea either that Mat knew Else personally (probably told herself "Why am I not surprised?" though)

She says so herself, killing without a good motive isn't her style, and she had no reason to kill Else just to steal her appearance for a few minutes. She would not have found her anyway, Else was already on the way home.