Eddie Jones' side are bidding to create history by becoming the first team to win the title for three successive years, but Lawes insists that there is a lot of rugby to be played before they can celebrate that feat.
Therefore, Lawes claims nobody in the Red Rose squad is looking beyond the opening game against Italy in Rome on Sunday.
On aiming for a triple triumph, he said: "No, honestly. That is a long way away and we've got a good few games to get through to achieve that.
"That is a goal at the end of a process. We're thinking about Italy and that is our main focus right now."
England will expect to get off to a winning start this weekend, but Lawes insists that they will not be taking the Azzurri lightly.
"No game is easy. Honestly, on any given day any team can produce an upset or an unbelievable performance,' added Lawes. 'You never know what team is going to turn up.
"We have got to keep our eyes on the prize and make sure that we are prepared for Italy."