The ban ends on November 21, and he has also been disqualified from the Olympic Games. Lynch has also been ordered to pay €1305 towards the tribunal's costs.
In reaching its conclusion the Tribunal concluded the substance at issue - Capsaicin - was a "Medication Class A" rather than a "Doping" substance based on its interpretation of the list of prohibited substances.
Lynch has 30 days to appeal this decision to the Court of Arbitration for Sport (CAS).
Horse Sport Ireland Chairman Joe Walsh said that the expert group established by the Board of Horse Sport Ireland to advise on the eradication of prohibited substances and practices from Irish equestrianism would take the details of the FEI decision into account when issuing their recommendations to the board.
"This group has meet already under the Chairmanship of Dr Gordon Holmes and I expect them to report before year end. Horse Sport Ireland will implement all of their recommendations rigorously," he said.
Walsh said that the group would also be advertising for submissions from interested parties and members of the public in the coming days.
"As the new Governing Body for the sport I want to ensure people that we will be relentless in dealing with this issue," he said.