The battle between the schools began in 1957.
After the 57th match a fortnight ago, both have won 17 and drawn 20. Three were abandoned due to rain.
Lindisfarne's director of sport, Derek Martin, says Dowie's "a very promising all-rounder", considering the teenager had scored 80 off 52 balls for the first X1 against Cornwall a day before the Scots exchange.
Martin, who has represented New Zealand Universities and Otago, says: "AJ has the attitude and ability to become a class cricketer.
"To take eight wickets within a two and a half hour spell is no mean feat. AJ showed outstanding control and made life extremely difficult for all the Scots' batsmen."
What are AJ's plans?
"I have been very lucky," he says. "I decided at the age of 12 that cricket was my forte and I was encouraged by the likes of Mitchell McClenaghan, when playing for Cornwall, to follow my dream."
But for now education is his priority.