The Australian cricketers are in charge of the second test in Adelaide, reaching 111 for five at stumps on day three, a lead of 273 runs over South Africa.
Australia managed to dismiss South Africa for 388 with captain Graeme Smith out early for 122 with Ben Hilfenhaus snaring three wickets, while Siddle and Lyon claimed two each.
Michael Clarke is on nine not out and Mike Hussey five not out at the crease heading into day four.
South Africa battled to 388 on the third day, after an injured Jacques Kallis combined with Faf Du Plessis to guide the visitors past the follow-on before Kallis was eventually out for 58.
South Africa started the day on 217 for two, chasing Australia's first innings of 550.
But Peter Siddle led a strong Austraila bowling effort which resulted in South Africa losing five wickets in the first session for the addition of only 56 runs in Adelaide.
South Africa face an uphill battle to save the second test with Kallis unable to bowl.
The Australian pace bowler James Pattinson left the field before the end of the first session to have treatment for a side strain.