White Sox reliever Jimmy Lambert doing his share

“The No. 1 thing in the big leagues is availability,” said Lambert, who already has made 12 appearances this season.

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Jimmy Lambert of the White Sox throws against the Angels last season.

Right-hander Jimmy Lambert led all White Sox relievers with 12 appearances entering play Monday.

Ronald Martinez/Getty Images

TORONTO — Right-hander Jimmy Lambert led all White Sox relievers with 12 appearances entering play Monday. That says the team hasn’t gotten enough lengthy outings from its starters.

Lambert not only has made himself available, but he has pitched effectively, with a 3.27 ERA and 16 strikeouts to go with six walks in 11 innings.

‘‘The No. 1 thing in the big leagues is availability,’’ Lambert told the Sun-Times. ‘‘If you’re available, you’re way more valuable than if you’re not available. So you do what you can to be available every day.’’

Lambert has pitched on consecutive days three times since April 10 and has gone more than an inning twice. Lucas Giolito has pitched six innings three times, Dylan Cease twice and Mike Clevinger, Michael Kopech and Lance Lynn once each, putting plenty of work on a bullpen that had a 6.22 ERA in the Sox’ first 22 games (although it was 2.86 in the last six games entering the series opener against the Blue Jays).

‘‘You just have to have good communication with the manager, pitching coaches and trainers,’’ Lambert said. ‘‘Trainers have done a very good job keeping me as ready as possible.’’

For any reliever, being available is dependent on knowing his arm’s limits, when to push it and when to back off.

‘‘There is definitely a fine line,’’ Lambert said. ‘‘But I also think that our mind is very strong. And sometimes we guard ourselves too much. Our bodies are capable of more than we think they are, and sometimes testing our limits is a good thing, see how far we can go.

‘‘You don’t want to get hurt — that’s in the back of everyone’s mind — but sometimes you have to test limits.’’

Lambert missed most of the 2019 season after having Tommy John surgery, and he dealt with a strained right forearm in 2020. Having been through such adversity has its benefits now, he said.

‘‘For sure,’’ Lambert said. ‘‘But I think also with injuries, when you’re truly injured, it allows you to learn your body. And the experience of being injured helps you understand the difference between soreness and injury.’’

Anderson close to rehab assignment

Shortstop Tim Anderson worked out without a brace on his left knee and likely will head to Triple-A Charlotte for a rehab assignment any day now.

The Sox are 2-10 since Anderson went down with a sprained left knee. While saying there is much more to the Sox’ recent slide, manager Pedro Grifol said Anderson is ‘‘the heart and soul of the club. As he goes, we go. He’s the energy.’’

Third baseman Yoan Moncada (back), meanwhile, still has no timetable for a return.

Kelly reinstated; Giolito on bereavement

Reliever Joe Kelly (strained groin) was reinstated from the 15-day injured list, and Giolito was placed on the bereavement list. Grifol said Giolito won’t miss a start.

Video gamer

Giolito said he uses a video game to prepare for his starts.

‘‘I do my video-game thing with ‘MLB: The Show,’ so I can really kind of commit that stuff to memory and practice my sequences,’’ Giolito said on the Chris Rose Rotation podcast. ‘‘ ‘Oh, I’m in this situation, what are the pitches that I feel very confident to get this guy out [and] get out of this situation?’ ’’

Hendriks sighting?

Closer Liam Hendriks, who is cancer-free and working toward a return, might make an appearance in Chicago on the upcoming homestand before returning to Arizona to pitch in games, Grifol said.

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