Often, the same fans would ask little Marcus to sign their baseballs or cards as well and he would oblige, in print because he hadn't yet learned to write in script.
Now, as Marcus prepares to graduate from Eustis High School in Florida, where his dad was his varsity coach, there is one autograph experience that really stands out in Lemon's mind.
Recently, a young fan came up to him after a game and handed him a Texas Longhorns baseball cap to sign. Marcus had just announced his decision to commit to Texas, the defending College World Series champion.
"It meant a lot to me that he even knew I was going there," Marcus recalled. "He thanked me for signing it but I was even more thankful to him. I felt honored to sign that hat."
Marcus' future as a Longhorn, however, is not engraved in stone. The upcoming First-Year Player Draft could change those plans.
The 5-11, 175-pound shortstop is expected to be selected in the first few rounds, possibly as high as a supplemental first-round pick.
"He's a very good baseball player with a blue collar work ethic and very, very good instincts," said one scouting director. "I think he could be a steady guy that goes up the ladder to the Major Leagues. I really like the way he plays."
In his 31-game campaign as a senior at Eustis, Marcus hit .451 with six homers, 24 RBIs and 23 steals, having been caught just once. He also drew 33 walks while striking out five times.
A line drive hitter who can drive the ball to all fields, he is a fine defensive shortstop with good hands and a quick release. What he lacks in pure speed he more than makes up for in savvy baserunning ability.
But what impresses people most when they watch Marcus Lemon play is his obvious love for the game and the joy with which he plays. If he lacks one outstanding tool, he balances that with his ability to do everything well.
The instincts are probably partly genetic and partly learned from working with his dad on a daily basis for pretty much as long as he can remember.
His earliest baseball memories are of hitting a Wiffle Ball in the backyard as his dad taught him to hit left-handed.
Lemon, 51, was a first-round draft pick in 1972 who went on to become a popular center fielder for the White Sox and especially the Tigers, and was a career .273 hitter. But shortly after he retired in 1990, when Marcus was just 2, the elder Lemon was diagnosed with a disease which subsequently forced him to undergo removal of his spleen. He has battled the side effects of the illness and several hospitalizations, one as recently as this past spring training, with his family by his side.
But he still coaches the Eustis team, which has won two Florida state titles, with the passion and energy with which he patrolled the outfield in his prime. In addition, he's president of the Florida Amateur Athletic Union.
He's worked tirelessly with youth athletics in central Florida, his wife Gigi by his side every step of the way. Her degree in computer science from Michigan has made her the technical whiz of the family business (as well as the official statistician for the Eustis varsity).
Lemon also coaches a very successful 18-and-under travel team, Chet Lemon's Juice, which has featured the likes of such players as Milwaukee Brewers stars Prince Fielder and Rickie Weeks, Kansas City Royals top prospect Billy Butler, and the New York Yankees' top pick from 2005, C.J. Henry, a fellow shortstop who lived with the Lemons for a month last summer.
Marcus has played for the Juice, as well as various high-level summer all-star squads, including the USA Baseball Junior National Team that won the silver medal in the summer of 2005 with him at starting shortstop.
"He's always competed against the very best players and that is why I have confidence he will excel," Lemon said.
While Marcus has played for other coaches on some of the summer teams, his dad has been his primary coach ever since those days of backyard wiffle ball and he wouldn't have it any other way.
"I think he's a great coach," Marcus said. "He's tough and strict, yet you can talk to him and he'll always listen with an open mind."
Still, Lemon has always been aware that as dad and coach he walked a fine line.
"I think it's been harder for me than it has for him," he said. "I told him when he was 11 or 12 that if the coach/player relationship ever interfered with the father/son relationship I'd stop coaching him."
That never happened, though obviously it will by the end of this summer, whether Marcus heads to Texas in the fall or to a Minor League team will be determined before then.
Draft day will likely find the Lemon family thousands of miles from home in Albuquerque, New Mexico, where Marcus is slated to play in a high school all-star game which takes place on June 7.
"I'll help him make what I think is a good decision if he asks me to, but ultimately it has to be his decision and he has to be happy when it's done," Lemon said. "But I think whatever decision he makes will be the right one because his motives will be in the right place. It's not about the money. It's about his love of the game."
And Lemon has no doubts that Marcus will be just fine wherever he winds up.
"He has a work habit second to none, not only at baseball but at everything he does," he said. "And he takes nothing for granted."
That work ethic is evident in the numbers. Not just the batting average but the 4.2 GPA he boasted as a senior.
And when it's time to relax, Marcus doesn't pick up the iPod or the remote control like some kids, but rather a paintbrush and pad. He loves to paint and draw, with a particular interest in abstracts these days.
"That's one talent he didn't get from his dad," Lemon laughed. "I can't even draw a straight line."