I'm not entirely clear on Lady Jane's motivations. I assume she's recognized the attraction between Grayson and Mina, is jealous of Mina, and is trying to hurt her by having Lucy seduce Jonathan. But that's just absurdly overcomplicated. And if she breaks up Mina and Jonathan, wouldn't that just drive Mina further into Grayson's arms? Isn't Jane shooting herself in the foot?
I've entertained the thought that this is part of the Order's recruitment of Harker -- Lucy would be easier to control than Mina, and thus pose less threat to the Order -- but I don't believe that Lady Jayne is aware of Browning and Davenport's scheme to recruit Harker.
I've instead come around to the idea that Lady Jayne is manipulating Lucy into murdering Mina, thus eliminating her romantic rival for Grayson's affections. When Jonathan spurns Lucy's advances, and with the seeds of distrust already planted by Lady Jayne, Lucy will take out her anger on Mina. That's still a rather overly complicated scheme, but I don't see another endgame that makes sense.