Shane Breen and the Irish-bred Cos I Can were sixth in Friday's competition and also took a seventh place in the Welcome Stakes at Birmingham on Thursday, while Lynch had a ninth place in Thursday's Two Phase competition on Contifex.
The Horse Of The Year Show's Grand Prix takes place tonight at the Birmingham arena, with €28,000 on offer as prize money.
Cork's Billy Twomey is also representing Ireland at the British show.
• The country's pony team won the Swiss Nations' Cup at Chevenez on Friday, and as a result finished joint first in the 2011 Pony EY Challenge Cup with Belgium.
With five teams battling it out for the Cup, Ireland finished the first round on a zero score, with Germany and Belgium joint second, and in the final round the Irish quartet incurred just eight faults to take the trophy ahead of second-placed Switzerland on 12 faults and Belgium on 16.
Ireland had a double clear round from Max O'Reilly-Hyland and Rock Dee Jay, while anchorman Bertram Allen and Acapella Z went clear in the first round but didn't need to jump in the second.
Irish opener Tom Foley and Crown Jewel went clear first time out and picked up four faults in the second round, while Eoin McMahon and the Irish-bred Another Destiny had a single time fault on their first round and four faults on the second.