Coe, the two-time 1 500m champion who heads the organising committee for the 2012 London Games, and Olympics Minister Hugh Robertson said on Friday they have written letters supporting the British Olympic Association's hardline doping rule.
The letters were sent to the Court of Arbitration for Sport ahead of a hearing in London on March 12.
The BOA is challenging a decision by the World Anti-Doping Agency, which ruled in November that the lifetime ban was "noncompliant" with the global code and amounts to a second sanction.
The BOA contends the rule, which has been in place since 1992, is a matter of eligibility.
"I have written a supportive letter from a personal perspective of somebody who has a long and fairly robust history, and an unreconstructed history some might say, on this," Coe said. "It is a personal view."
Robertson said he underlined the government's support for the BOA's right to select its own team.
"Secondly, it remains this government's policy to support a lifetime ban for drugs cheats," he said at a news conference marking the six-month countdown to the London Games.
Britain, the only country that enforces a life ban, could be forced to drop the rule ahead of the London Olympics if it loses its case.
Among British athletes currently covered by the BOA rule are sprinter Dwain Chambers, who served a two-year ban in the BALCO scandal, and cyclist David Millar, who was suspended for two years after testing positive for EPO.
If WADA wins the case, Chambers and Millar will become eligible to compete in London.
The BOA's regulation came under scrutiny after CAS threw out the International Olympic Committee rule that bars athletes who have received drug bans of more than six months from competing in the next games.
The CAS ruling cleared the way for American 400m runner LaShawn Merritt - who completed a 21-month doping ban last year - to defend his Olympic title in London.