I'd go:
Lloris
Walker
Dawson
Chiriches
Rose
Lennon (Eriksen 60)
Capoue
Dembele
Holtby (Sigurdsson 80)
Lamela
Soldado (Adebayor 70)
And to give some justification to it all:
Southampton will move the ball around well in the midfield so we need players in the middle who can hassle them and make things tricky. Holtby isn't a natural winger, but we'll need someone who will drift inside and make an extra man for us in the centre, which is exactly what he'll do. In a deeper role, he'll also pass the ball better to help us retain possession and create chances on the counter. Dembele and Capoue will provide strength and steel in the middle of the park, Lennon the width and the more direct threat. Get Capoue to sit back and stay close to Lallana, don't let him run at Dawson.
Up front, we'll have two strikers. Lamela I feel is most suited to playing up front in the Aguero/Suarez role alongside another striker, so let's give him the chance to use his pace and run in behind the opposition. That will help peg Southampton back a little and relieve some of the pressure on our defence. It will hopefully give him a chance to show us his finishing ability that he demonstrated at Roma and also the passing ability that we've seen in flashes as he'll be closely supported by Soldado or Lennon making runs alongside him when he's on the ball. Having an extra striker will mean that Soldado isn't completely isolated when in possession, and that opposition defenders will be dragged away from Soldado especially when Lamela who likes to run with the ball is in possession.
Later in the game, we bring on Eriksen for a bit more creative spark, as gaps will be starting to appear that we can pick out passes into. At this point, Lamela will shift a bit further wide, with Eriksen cutting in from the other flank and then Holtby, Dembele, Capoue making up a three man midfield. As the opposition defence begins to tire, the last thing they'll want to see is a big, fast striker with unpredictable movement coming on, which is why we bring on Adebayor in the later stages. Finally, Sigurdsson can come on to replace Holtby who will surely have tired himself out by the 80th minute.
Things are a little different if we're losing, because if they put 10 men behind the ball (unlikely at home) then we'll need Lennon to keep width to our play and create more space for our attackers, perhaps bring on Defoe for Dembele or Holtby in that situation. Or if they throw everything forward in search of an equaliser to an early lead we've taken, then Lennon's pace on the counter will be useful. But generally, this is how I'd like to see us play. We need a win today, we can't afford to sit back and hope for the best. Let's go for it.