Tour captain Sam Warburton skippered the Lions in the first two Tests against Australia in 2013 before injury ruled him out of the decisive third match.
And the Wales flanker, who has carried a knee injury into the tour, must make do with a place among the substitutes against New Zealand at Auckland's Eden Park.
In his absence, Ireland's O'Mahony has secured the prestigious honour of leading the tourists versus the reigning world champions.
