Harmer completely dominated day five of the Test, taking 6-16 and appearing virtually unplayable as Australia were all out for 111 on a deteriorating Newlands pitch.
His effort came just a day after Lyon took 2-101 from 44 overs, as South Africa recovered from 4-140 and a lead of 40 runs to setting Australia 288 for victory.
But captain Pat Cummins suggested it was not necessarily fair to compare the two figures, and insisted his offspinner had bowled well with the series on the line.
"It's a hard one. There's obviously a little bit of help being day five as it was yesterday," Cummins said after Australia's 176-run loss.
"I thought Nathan controlled the game really well.
"There are days where he goes and takes five or six wickets, but one of the big keys to why we love him on our side is that it makes everything else function well.
"For most of the game, they went at 2.5 (runs) an over. We were really controlling that, and Nathan was the key to that."
Cummins also backed Lyon's performance in Australia's first Test win in Durban, before heavy cloud cover prompted Scott Boland to come in for him in Gqeberha.
He was not the only Australian bowler to have a difficult tour.
Cummins himself took just six wickets at 54.66, with only a 2022 tour of Sri Lanka proving less fruitful in his career.
That was partly due to less lively wickets in Gqeberha and Cape Town, prompting Cummins to go shorter than in recent years, with little sideways movement on offer.
The quick at one stage went 373 balls without a wicket, in what was the longest drought of his Test career.
"Hard to know (what happened), I was really happy with how I bowled and batted in in Durban, the first Test," Cummins said.
"I don't think it much changed the last two or three Tests. Ball speed, false shot percentage and all those things stayed relatively similar.
"I've had series where I've felt a little bit injured or technique (issues) or whatever, and I've taken wickets and you feel a bit further away from it.
"But I was actually, overall, generally happy with how I bowled. Tried lots of different things on relatively benign wickets, but just couldn't get it done."
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