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21-year-old Thornton was a substitute in both Ireland's first Group 4 qualifier - September's 3-0 win over Cyprus in Kilkenny, and their last game, the 4-2 loss to table-toppers Switzerland in Bern.
Thornton made his Under 21 debut against Scotland in February last year - winning a further 11 caps since, but failing to score from his midfield berth.
18-year-old Dawson, a regular in the Leicester reserves this season, has represented Ireland at under 17, 18 and 19 levels after being spotted playing for Portmarnock FC in Dublin.
The Foxes' Academy director Jon Rudkin told the club's website: "Stephen had a terrific pre-season and he has a great work ethic. The call-up is just reward for him and hopefully he will gain great experience from it.
"He knows where his pluses are around the pitch and he also knows what aspects of his game he needs to improve on. He is a very determined individual and we wish him all the best for his trip."
Thornton's fellow Black Cat Stephen Elliott also pulled out of the Irish squad earlier this week. Givens' side are currently third in the table behind the Swiss and French.