Despite Ashton Agar's side injury and the absence of Adam Zampa due to paternity leave, Swepson has featured just once for Australia during the ODI series in Sri Lanka.
Swepson returned figures of 1-58 from 10 overs in the low-scoring second ODI, with Sri Lanka now leading the five-match series 2-1.
Australia left out the left-arm leg-spinner for the third ODI in favour of retaining Matthew Kuhnemann, casting doubt as to whether Swepson will be used during the Test series.
Swepson struggled on the Test tour of Pakistan earlier this year, returning figures of 2-266 across the two matches.
Lyon has loved seeing the progression of spin trio Kuhnemann, Tanveer Sangha, and Todd Murphy, but believes Swepson is the best placed for the Tests against Sri Lanka.
"I do feel a bit for Sweppo. It's pretty hard when you get one crack (in the ODI side) and then you miss the next," Lyon said.
"I was really happy and pleased with our partnership that we bowled together in Pakistan.
"I know he probably didn't have the ideal tour that he wanted, but he's a very team-focused player and we got the right team result.
"I love the way he's a team-first bowler, he's a team-first player, and he'll do anything for the team.
"He works his absolute backside off."
Lyon said Australia's 1-0 Test series win in Pakistan earlier this year would give the team great confidence ahead of the Tests against Sri Lanka, which start in Galle on June 29.
"It's purely the belief that our process and what we're doing is starting to work," he said.
"We all know how hard it is to win games of Test cricket away from home. I think the sub continent added an extra 20 per cent on top of that.
"The pure belief that we were able to hang in there for 15 days of really hard Test cricket in the subcontinent and end up with the right result was the biggest thing.
"The Australian Test team has a lot of belief coming over here and performing in these difficult conditions."
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