Lancaster has also stated he expects Toby Flood to be fit, despite the injured Leicester fly-half being withdrawn from both the Premiership semi-final and Saturday's final.
Phil Dowson took a heavy blow to the head during England's 57-26 victory over the Barbarians on Sunday but Lancaster expects he will also be available to tour.
Tuilagi was penalised in the second minute of Leicester's Premiership final defeat to Harlequins on Saturday for lifting Care off the Twickenham turf in a tackle.
Rugby's disciplinary authorities are hot on incidents such as this and the citing officer has four working days from receipt of the match video.
But Lancaster is hopeful Tuilagi will not be cited and therefore free for England's three-Test series with the Springboks.
"We have not heard anything. Looking at the incident I am pretty confident he will be fine but we will wait and see," Lancaster said.
"Phil Dowson had a bang to the head but he is up and walking around in the changing room. We have some time before the first Test but at the moment he is looking okay.
"Toby hurt his groin kicking prior to the game and Leicester chose not to risk him. He will turn up in camp tomorrow and we fully expect to take him on the tour."
England ran eight tries past the Barbarians today, with wing Chris Ashton rediscover his scoring form with a Twickenham hat-trick.
Dylan Hartley, Christian Wade and Richard Wigglesworth also touched down before replacement Jonathan Joseph marked an impressive cameo with two tries.
Ashton had not scored for six previous Tests and, although this was not a capped game, the hat-trick is the perfect confidence boost ahead of the South Africa tour.
"I am pleased for Chris that he has got the three tries," Lancaster said.
"His work rate off the ball is tremendous. Sometimes he can work and not get the off-loads but today he did and it is great.
"Credit to him for working hard and getting the rewards.
"As a team we recognise areas we still want to improve and tighten up on but overall he and others did well. I am pleased."
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