Kevin Fennell, however, had a different plan for her, although both didn't know it at the start.
The 21-year-old A's ballboy, stationed near Oakland's bullpen throughout the game, spotted Lynch nearby in the stands and, after putting his glove on a foul ball, passed by a line of fans and handed it to her.
"He looked at me and pointed," Lynch recalled. "I said, 'Me?' and he came over and gave me the ball."
Later in the game, an eventual 4-3 Oakland win over Tampa Bay, Fennell did it again, at which point the A's television crew caught on to the act and shared it with its audience -- including those friendly with Lynch.
"People kept texting and calling me," Lynch told MLB.com by phone on Friday. "I thought it was so funny. I can't believe how much attention this has all been getting."
Although video only shows Fennell handing off two balls, he admitted the count actually grew to four. Lynch, though, says she walked away with five balls, the last of which came via messenger from the bullpen, reading, "How about a phone number for our Ball Man, Kevin?"
Fennell not only received the digits, but he's also already communicated with Lynch via text message to set up a date.
"We're going to get drinks next week," he said.
The blushing Fennell, who on Friday afternoon was nervously preparing in the A's clubhouse for a television interview with MLB Network, is suddenly quite the popular face. At the same time, he's also gotten plenty of slack for Thursday's events.
"Everyone was booing because he was giving all the balls to me," Lynch said, laughing. "I don't know anyone who's gotten five foul balls in one game before. I thought I was going to get mauled or something."
Instead, she got a date. And Fennell said he made amends with the booing crowd.
"After the game," he said, "I gave out about 10 balls."
That doesn't mean A's players are cooling off the banter just yet, though.
"It's OK," he said. "As long as it works out with Jacki."
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.