You can debate on how much or little Lallana might improve a Saints side, but personally I don't think he makes a significant enough improvement. Besides, he's not the player we don't have. He's not a player with great vision, say like Fabregas [who is in shocking form at present], or dare I say it, Rickie Lambert in his midfielder guise, and we have Mane who can do Lallana's old job of putting the wind up defences.
As I mentioned before, all the top 6 sides have playmakers. Even Swansea have Shelvey, but Saints aren't going to attract them. Which is why I suggested Sissoko. Of course, that's from the pool of players I know well. I'm sure Saints have their eyes on several unknown to me.