While Lucas can be improved upon, I don't think we'll be signing another DM anytime soon, especially with a new-look defense which enables us to play a higher line and recover quicker, thereby downplaying Lucas' main weakness in his game, his lack of athleticism, while pushing him more forward where his ability to recycle the ball gets more traction.
In midfield, I can use us converting and moulding Ilori into a DM. After all, he has played there before, has the perfect set of attributes (pace, positioning etc.), and is young enough to be coached into the role. Instead, I can see us going for Will Huges in the winter window, as the long-term successor to Gerrard, a position that is arguably harder to fill than a DM in Rodgers' system. Gerrard and Allen, and Henderson in a pinch, can be called upon to cover.