Twelvetrees comes in as temporary cover for London Irish centre Jamie Joseph who is struggling with an ankle injury, while Burns takes the place of Jordan Turner-Hall as the Harlequins midfielder is staying with his club for treatment on an inflamed knee.
Burns is currently the leading scorer in the Aviva Premiership and had been touted as a possible squad member prior to Lancaster's initial announcement last month.
The 22-year-old has been in outstanding form for his club, with Gloucester director of rugby Nigel Davies suggesting he is every bit as good as his former Scarlets charges Rhys Priestland and Stephen Jones.
"I've worked with a lot of 10s and Freddie's right up there," was Davies' assessment of his young playmaker.
"He's really maturing. As a 10 it's not all about you: it's about how you manage the team, and he's really starting to do that now."
Lancaster originally opted to name Toby Flood and Owen Farrell as his first-choice fly-halves but now Burns will get a chance to impress in the build up to the first of four Twickenham encounters this month and next.
"Freddie has been playing well in the Aviva Premiership and, with Jordan needing to stay at Harlequins for treatment, we are keen to have a look at him," said Lancaster.
"JJ is continuing his recovery from an ankle injury and this is a good chance to get Billy in for training."
With both Dylan Hartley and Courtney Lawes definitely unavailable for the opening clash with the Fijians, George Robson and David Paice will remain with the squad, although the Northampton duo won't be heading back to their club either.
"As last week, George Robson and David Paice come in as injury replacements for Courtney Lawes and Dylan Hartley. Both will be assessed and treated in camp and it is important that they stay with the squad as much as possible," added Lancaster.
"We had a productive week at St George's Park and got a lot of work done. Now we are back at Pennyhill we will sharpen our focus towards Fiji on Saturday."
Revised England squad
Forwards - Props: Dan Cole (Leicester Tigers), Joe Marler (Harlequins), Mako Vunipola (Saracens), David Wilson (Bath Rugby) Hookers: Dylan Hartley (Northampton Saints), Tom Youngs (Leicester Tigers), David Paice (London Irish) Locks: Mouritz Botha (Saracens), Courtney Lawes (Northampton Saints), Tom Palmer (London Wasps), Geoff Parling (Leicester Tigers), George Robson (Harlequins) Back-rows: James Haskell (London Wasps), Phil Dowson (Northampton Saints), Tom Johnson (Exeter Chiefs), Ben Morgan (Gloucester Rugby), Chris Robshaw (Harlequins), Thomas Waldrom (Leicester Tigers), Tom Wood (Northampton Saints)
Backs - Full-backs: Mike Brown (Harlequins), Alex Goode (Saracens) Wings: Chris Ashton (Saracens), Ugo Monye (Harlequins), Charlie Sharples (Gloucester Rugby) Centres: Anthony Allen (Leicester Tigers), Brad Barritt (Saracens), Jonathan Joseph (London Irish), Billy Twelvetrees (Gloucester), Manu Tuilagi (Leicester Tigers) Fly-halves: Owen Farrell (Saracens), Toby Flood (Leicester Tigers), Freddie Burns (Gloucester) Scrum-halves: Danny Care (Harlequins), Lee Dickson (Northampton Saints), Ben Youngs (Leicester Tigers)