"He's taking all those steps that'll keep us considering him and figuring out if it's going to be something we can put in with what we have," Matheny said on Sunday. "He's answered a lot of the questions on what he can handle, which is the health and getting built up. But it's just going to be a matter of how he responds, a day like today after he throws, see how he feels and take it from there."
In Saturday's outing, Lyons allowed two runs on three hits, walked none and struck out five. He threw 44 of his 58 pitches for strikes.
"I think I feel good with where I'm at," Lyons said. "I feel good with my pitches. I think my body is a lot closer to where I wanted it to be. I think it's just one of those things that will keep getting better. But there's no big need for [more] rehab in my opinion."
This has been Lyons' second stint on the disabled list this year, as he spent the first few weeks of the season recovering from left knee surgery. When healthy, Lyons has made two appearances for the Cardinals.
Wong still ailing
Pulled from Saturday's loss after three innings due to soreness around his left elbow, Kolten Wong remained out of the lineup on Sunday. But Matheny described the club as "very optimistic" that Wong won't be sidelined long, particularly since it is not his throwing arm that is being affected.
"It'll still be a day-by-day, but it seems like something that took a good step forward last night, so that's positive," Matheny said. "Everything showed up today much better and the doctors are very confident that as long as it just keeps feeling better, it's kind of a day-to-day thing."
Wong did report feeling a "pop" while taking warmup swings in the on-deck circle before his first at-bat. The Cardinals do not believe, however, that Wong is dealing with a structural issue. Greg Garcia drew the start at second base in Wong's place on Sunday.
• Left-hander Zach Duke, who underwent Tommy John surgery in October 2016, will throw three bullpen sessions at Busch Stadium this week before relocating his rehab to Jupiter, Fla. There, Duke is scheduled to face hitters for the first time since having his elbow operation.
If all goes well, Duke hopes to begin a rehab assignment in July and perhaps be back pitching for the Cardinals by August. That would represent an accelerated timeline, as most Tommy John patients require about a year to recover.
• Left-hander Marco Gonzales threw 6 1/3 scoreless innings for Memphis in a win on Saturday. Since wrapping up his recovery from elbow surgery and rejoining the Triple-A club, the Cardinals' No. 19 prospect has allowed one run and seven hits over 13 1/3 innings.