I don't think Leicester will lose this. What could happen is that the #3 and #4 positions in the table could change. Manchester United, West Ham United, and Liverpool have all come on strong this second round and are challenging for those Champions League slots.
Leicester's last four matches are against Swansea (at home in a match they should win), Manchester United (away that will be tough), Everton (at home but the Toffees' play better away from their homefield), and lastly at Chelsea's pitch of Stamford Bridge.
It doesn't get easier for Tottenham as well. They battle West Brom at home and they should win that handily. They face Chelsea at Stamford Bridge too. Southampton at home and Newcastle for their final match that is away. You bet the Magpies will want to win this as they are fighting to get out of relegation. Regardless where they are at that point, expect Newcastle to give it a good fight.
Arsenal should have an easier time but I really can't say for their form or morale. But they play Sunderland away, Norwich at home, Man City away, and their season ender at the Emirates against Aston Villa. Three of their last opponents are in the lower rung with only Aston Villa sure to be relegated.
Man City plays Stoke at home, Southampton away, Arsenal at home, and Swansea away. You really don't know what you're getting with the Citizens. I figure they're in a battle against everyone with no sure win.
The Red Devils play Leicester at home, Norwich away, West Ham away, and at home against Bournemouth. All will be tough battles. They will have their hands full.
West Ham plays in succession West Brom (A), Swansea (H), Man United (H), and Stoke (A).
Lastly, Liverpool is the only team in the top seven with five remaining fixtures. Newcastle (H) where they renew acquaintances with Rafa Benitez who is now manager of the Magpies. Swansea (A), Watford (H), Chelsea (H), and West Brom (A). If they play up to form, they could collect all 15 points and muscle their way to the Top Four.