Lallana latched on to a Rickie Lambert header to score the first after 35 minutes and was on target from close range in the 54th minute as Nigel Adkins' men took their unbeaten run to nine league matches.
Second-placed West Ham are only ahead of Reading on goal difference as the Hammers drew with Doncaster while the in-form Royals beat Leicester.
Sam Allardyce's men made a great start as Kevin Nolan scored in the ninth minute, but Rovers hit back through James Coppinger (73).
Reading recorded their eighth straight win to join West Ham on 66 points, as goals from Mikele Leigertwood (15), Jason Roberts (75) and Simon Church (89) put them in control before Neil Danns scored a late consolation for the Foxes.
Blackpool dropped out of the play-off places after a 3-1 defeat at Peterborough.
Posh were looking to avoid a third straight loss and led 2-0 at half-time with goals from Tyrone Barnett (27) and Paul Taylor (43). Nouha Dicko pulled one back with 10 minutes to go, but George Boyd's 86th-minute strike from Tommy Rowe's cross made the points safe for Darren Ferguson's team.
Brighton are up to fifth as Vicente's double in the final 15 minutes earned them a 2-0 win over Portsmouth, who have now failed to win any of their last eight.
The midlands derby between Coventry and play-off hopefuls Birmingham at the Ricoh Arena finished 1-1 as Gary McSheffrey and Marlon King scored against their former clubs. The result left the Sky Blues still in the bottom three.