Lyon played a leading role in Australia's 4-0 Ashes Test series win over England, playing in all five Tests and capturing 21 wickets at 29.23.
Lyon is Australia's most successful off-spinner with 290 Test wickets.
"It's a tremendous honour to be selected to captain the Prime Minister's XI and captain alongside the likes of past greats including Brett Lee, Michael Hussey and Ricky Ponting," Lyon said.
Former Test wicket-keeper Brad Haddin will coach the PM XI for the match at Manuka Oval on February 2.
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