Gareth Southgate is in temporary charge for the next two games following the departure of Sam Allardyce.
The first of these is Friday's World Cup qualifier against Scotland.
"We are ready to fight for him [Southgate] in the matches. Hopefully he will do well enough to get the job on a permanent basis," said Lallana.
"It would be nice for Gareth and for us quite soon to know whether he's going to get the job," added the 28-year-old.
"You can build towards having a certain identity that your manager wants you to have.
"That's what a manager is there for. I'm sure over the next few days the manager will be telling us what he wants for the Scotland and Spain games [the latter is a friendly at Wembley next Tuesday]."
England have struggled at recent tournaments; failing to get out of their group at the 2014 World Cup and then suffering an embarrassing last-16 exit at the hands of Iceland at this year's European Championships.
"For quite a few years now we've not done brilliantly at major tournaments so it's up to us to maybe find an identity," said Lallana.
"Whether it's the mental side of the game at tournaments that we're struggling to cope with, we need to overcome that. Through good, hard work I think we can do that.
"You need stability. What you don't have at England is the time that you get at club level.
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"You can't prepare for a campaign as you would for a league over the course of the season. It's not possible so it's a different challenge."
England head into Friday's game against Scotland top of Group F with an unbeaten record, having won two games and drawn one.
England need a new permanent manager as soon as possible to try to create stability within the national side, says Liverpool midfielder Adam Lallana.