The visitors had scrum-half Danny Care yellow-carded for persistent infringement just before the break and Bristol took advantage when wing Anthony Elliott linked up with Rob Higgitt to put Lemi clear to score in the corner.
Ismael Bouzid, who had been booked in the first half, avoided a second yellow card after tripping Barry Douglas early in the second half and the defender was soon withdrawn to be replaced by Andrew Driver.
Scrum-half Care's yellow card in the 69th minute, for a shoulder charge on Marcus Horan, was particularly galling as, at that stage, Ireland only led 11-6.