Both men worked with the England set-up during this summer, joining training ahead of Test matches in unofficial batting consultant roles.
Mo Bobat, who was appointed as David Parsons' replacement in the performance director role at the end of the summer, said that the tour will give the ECB a chance to look at the next generation of English coaches coming through.
"This tour provides us a good opportunity to recognise two coaches who have excelled in their roles in county cricket in Richard and Jason, as well as two high potential newcomers in Jonathan and Marcus," he said.
"I'm delighted to have Richard on board as head coach for the Lions' tour of Australia. He's an excellent leader and provides great technical knowledge as a spin-bowling coach.
"Richard, Marcus and Jonathan all have experience of touring Australia with England as players so the advice they can pass on to our players will be invaluable.
Dawson, whose Gloucestershire side won promotion from Division Two of the County Championship this season, said: "I'm excited for this opportunity to coach the England Lions, working alongside some excellent coaches.
"It will be a challenging tour and one that the coaches and players will all learn a great deal from. Australia is a testing place to tour as an England player, both on and off the field. I look forward to working with some of this country's best young cricketers as they progress on the Performance Pathway."
The tour comprises five one-day games and three four-day games, with a day/night game against Australia A at the MCG the highlight.
England Lions tour of Australia, 2020
February 2 - One-day match v Cricket Australia XI (Metricon, Gold Coast)
February 4 - One-day match v Cricket Australia XI (Metricon, Gold Coast)
February 6 - One-day match v Cricket Australia XI (Metricon, Gold Coast)
February 9 - One-day match v New South Wales XI (Drummoyne Oval, Sydney)
February 11 - One-day match v New South Wales XI (Drummoyne Oval, Sydney)
February 15-18 - Four-day match v Cricket Australia XI (Blundstone Arena, Hobart)
February 22-25 - Four-day match v Australia A (MCG, Melbourne, D/N)
March 2-5 - Four-day match v New South Wales XI (North Dalton Park, Wollongong)