It does not boost the power of moves that do not use the damage formula (although the holder still takes damage) or self-inflicted confusion damage.
Source
Moves like Mirror Coat, Counter, OHKO-Moves, and set-damage moves ignore the damage formula. Hence, the damage wouldn't be boosted by Life Orb. However, the user seems to take recoil damage from those moves, though.
Replay
The opposing Wobbuffet used Mirror Coat!
(Blissey lost 15% of its health!)
The opposing Wobbuffet lost some of its HP!
The opposing Wobbuffet used Counter!
(Blissey lost 1% of its health!)
The opposing Wobbuffet lost some of its HP!
In both the cases, Wobbuffet (holder of Life Orb) seems to take recoil damage whenever using Counter or Mirror Coat. However, the damage is still direct, hence not boosted by Life Orb.
Hope this helps!
