Northhampton captain Hartley became the first player to be sent off in a Premiership final after abusing referee Wayne Barnes and calling him a cheat in Saturday's match against Leicester at Twickenham.
"With uncertainty over the availability of Dylan Hartley to tour and with the first of 10 matches only days away we had no option but to call up the additional player," Lions tour manager Andy Irvine said.
"Despite the circumstances we should congratulate Rory, who will join the squad tomorrow and fly with us to Hong Kong.
"A final decision on whether Dylan Hartley will take any part in the tour will depend on the outcome of any potential appeal."
Hartley had maintained that his expletive-filled comments were aimed at Leicester's Tom Youngs but at a hearing on Sunday the Rugby Football Union's independent disciplinary panel found against the New Zealand-born hooker.
"Calling a referee a cheat is an attack on his integrity and contrary to the core values of rugby and therefore we have taken a serious view and provided a serious sanction," judge Jeff Blackett, who headed the three-man panel, said in the ruling.
Hartley had already been warned by Barnes for speaking out of turn before the incident at the end of the first half that led to his sending-off. Northampton went on to lose 37-17.
The hooker was given a two-week ban earlier this season for striking Best, having served eight weeks for biting last year. Six years ago he was given a 26-week ban for eye-gouging which ruled him out of the 2007 World Cup.
The Lions fly to Hong Kong on Monday ahead of their three-Test tour of Australia.