Crisp, limited to just four at-bats this spring with tightness in both groin muscles, Lugo, who has played just two games since March 2 with tightness in his lower back, and Kielty, who has played just one inning since March 8 with tightness in his right calf, all got at-bats in the instrasquad games.
Sox manager Terry Francona said he will likely work all his players into the Grapefruit League finale on Wednesday against the Blue Jays.
"We'll make sure everybody gets in," he said. "It's a game where maybe [Sean] Casey picks up somebody where he doesn't normally. We'll have a full work day, also. We need to do it. It's not a normal travel day. We need a work day.
"I always think this happens too much in baseball anyway. You work hard all spring, then it's travel day, [and] guys get two at-bats. We don't want to lose it. We still have work to do."
Crisp, Lugo and Kielty will depart with the team on Wednesday afternoon for its trip to Japan.
"Coco has worked his fanny off," Francona said. "We don't think he's ready to play, and I don't think he does either. Saying that, he's done a great job to get to this point where we can take him with us. He can keep doing his baseball activities, and there's actually a chance he might be active. That's to be determined, but he's done a good job to this point.
"[Kielty's availability] will be determined. We can take 30 players. We're trying to cover exhibition games, regular-season games, winning games, having enough pitching and roster issues, and it's still the middle of March.
"'Lugy' was actually, in my opinion, a little bit farther along than these guys. He thought it was in his best interest to come here today and get some at-bats. I didn't tell him he had to. He's come along fine. And if we get over there, [Alex] Cora can pick him up if we need to."
Crisp and Kielty, both switch-hitters, had three at-bats against left-hander Felix Doubront in the Double-A game, before joining the right-handed-hitting Lugo in the Triple-A game to face righties Mike Jones and Chad Rhoades. Lugo also faced righty Ben Howard.
Crisp went a combined 1-for-4 with a home run and walk. Kielty was 1-for-5, and Lugo was 1-for-4 with a walk.
"I think it was a good day for all three of us," Crisp said. "I started off a little slow. I think all of us did, except for Kielty, who actually swung pretty good. Then I finished up good. [It was] good for us, confidence-wise.
"I'm going to go [to Japan on Wednesday] and play in the first games and see what's going on after that."
Crisp said he is not concerned with his legs, focusing more on hitting, but is not sure when he will be 100 percent.
"I don't know, because I haven't kicked it into [that gear]," he said. "It's still sore to the touch, so I guess not. Not excruciating, but like if you have a bruise. But I haven't got down and really tried to get after it, like 100 percent full speed. But I did try to steal that base and put enough into it to know I'm fine."
Kielty, who went from first to third on an outfield single, is pleased with how his calf has responded in the last few days.
"I was running with no pain," Kielty said. "It stressed me out for sure. I didn't know how quickly [it would heal], but it really took off in the last few days. I was really fired up to be able to run the way I did. I feel dramatically better. It definitely turned a corner, I think, to staying healthy."
The Sox's game against the Blue Jays at City of Palms Park on Wednesday begins at 12:05 p.m. ET.
Maureen Mullen is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.