The 24-year-old, who can play at centre and fly-half, was due to leave Buenos Aires for Australia on Wednesday.
The Lions have injury concerns over fly-halves Owen Farrell (dead leg) and Jonathan Sexton (hamstring), while centre Manu Tuilagi suffered a stinger in the victory over Queensland Reds.
Twelvetrees won his fifth England cap in last Saturday's 32-3 victory over the Pumas in Salta, scoring a try to cap an impressive individual performance.
The Gloucester player will be the fourth player to be called up by the Lions following the late arrivals on tour of loosehead props Alex Corbisiero and Ryan Grant and the Ireland wing Simon Zebo.
Twelvetrees had been due to start England's second Test against Argentina on Saturday.
England coach Stuart Lancaster will name his team on Thursday, with Bath's Kyle Eastmond now likely to step into the inside centre role to make his first Test start.
Twelvetrees is the second England player to be summoned to Australia from the tour of Argentina after Corbisiero received the call-up last Wednesday.
Lancaster said: "All the England players and management are delighted for Billy to get this great opportunity.
"He's played well for England this year, underlined that form with his display against Argentina at the weekend and goes with our full support and blessing."