Hours after England opened their QBE autumn campaign with a 54-12 win against Fiji, the Wallabies crashed to a thumping 33-6 defeat to France in Paris.
Lancaster expects the wounded Wallabies to bounce back with a vengeance at Twickenham on Saturday.
"We recognise the challenge that is coming our way," Lancaster said.
"There is bound to be a reaction from the weekend's performance against France. They are a side with character and resilience.
"I am sure if they have got a few players coming back as well they will be a different animal on Saturday. We need to make sure we are ready."
Australia endured a welter of criticism for their performances in the Rugby Championship but responded to that by pushing New Zealand to the brink in Brisbane before departing for Europe.
Lancaster will prepare England to face that side, who drew 18-18 with the All Blacks, rather than the Wallaby outfit that folded in Paris.
"It was only a couple of weeks ago they pushed the All Blacks and we are expecting that type of performance this weekend," Lancaster said.
"In this situation there is bound to be a reaction. They are a nation full of resilience in adversity and we need to be ready for it."
Alex Corbisiero and Jonathan Joseph have both returned to the selection mix for England this week after recovering from knee and ankle injuries respectively.
Lancaster and the England coaches will decide on Tuesday whether Corbisiero is ready for Test match action, after only his first start of the season on Sunday.
Corbisiero played 62 minutes for London Irish in their LV= Cup win against Sale Sharks and Lancaster may look to give him another run at club level.
That would leave England with Joe Marler and Mako Vunipola as the loosehead options, with Corbisiero potentially returning to the squad for the tougher scrummaging battle South Africa are likely to pose.
"(Forwards coach) Graham (Rowntree) went to watch the game yesterday. He was pleased with how (Corbisiero) went but it was his first start in five months," Lancaster said.
"We have got a decision to make and we will make it after training tomorrow. It is fair to say that is not a huge amount of time.
"Also, Mako did well for us in the game and what he has done in training has been impressive. He has been very accurate in everything he has done."
Joseph, who was unavailable for the Fiji game with an ankle injury, trained with England today for the first time since the summer tour of South Africa.
Centre Manu Tuilagi (foot) and lock Geoff Parling (shoulder) both sat out training but Lancaster was confident they would be fit to face the Wallabies.
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