'Eddie's going down there to win the series 3-0 and why not? It's realistic. It's a good squad,' the former fly-half told BBC Sport.
'The only thing is, it's the end of the season and a lot of the England players will be involved in Premiership and European finals. It's going to be a fascinating series.'
England's style of play under Jones has impressed Lynagh, who believes his Australian compatriot has restored a Red Rose arrogance.
'I think Eddie looks at the culture of English rugby and there is a perception that arrogance is part of it - so he's said we'll go and do that,' the 1991 World Cup winner added.
'He's not trying to 'Australianise' England. It would be wrong to do that, you have to come in and work on what culturally works within the country.'