The 16-year-old Thompson showed that she measures up on the course with her five-stroke victory Sunday in the Navistar LPGA Classic, which made her the youngest LPGA tournament winner.
Because she's not 18 yet, Thompson has two more stages of qualifying school to go through to become a member.
"She has kind of proven she can play out here," said Inkster, who at 51 was the oldest player competing. "She's proven she can handle the social part of it. I think they should give her full (membership).
"It's kind of silly, isn't it? I think it makes us (the LPGA) look bad, too. Now, you have to go to qualifying school? To me, that's silly."
LPGA Commissioner Mike Whan didn't seem inclined to let her skip the rest of qualifying school.
"Should Lexi qualify for LPGA membership via her Q-School performance, she will be an LPGA member for the 2012 season," Whan said in a statement.
The Floridian closed with a 2-under 70 Sunday to beat Tiffany Joh by five strokes to finish at 17-under 271.
Thompson shattered the age record for winning a multiple-round tournament held by Paula Creamer, who won in 2005 at 18. Marlene Hagge was 18 years and 14 days old when she won the single-round Sarasota Open in 1952.
The victory brought a piece of history and $195,000, $20,000 of which she plans to donate to the Wounded Project.
"This has been my dream like my whole life," Thompson said. "It's the best feeling ever."
Becoming a fixture on the LPGA Tour seems a foregone conclusion. The question now is when she'll be granted membership? Thompson will have to petition for an exemption of the 18-year-old age requirement.
The LPGA already granted her petition for qualifying school, and she won the first stage by 10 strokes in July with two more to go.
"We haven't even really talked about that yet," said Scott Thompson, her father and caddie.
"We'll worry about that as it comes, so we'll see."
Thompson, who turned 16 in February, led by five strokes entering the final round and built that to seven through 10 holes at the Robert Trent Jones Trail's Capitol Hill complex. Then came the teen's only big lapse on the pressure-packed day, bogeys on the next two holes that allowed Joh to surge within three strokes.
Thompson erased any concerns of a collapse with birdies on Nos. 16 and 17, and then the celebration and the kind words began for the new youngest winner.
"Seven years I've held that record. That's pretty good," Creamer said. "A lot of records are broken sooner than that. At 16, my goodness. She's played so many years out here."
Cool under pressure most of the day, Thompson and her father couldn't contain broad smiles as they approached the 18th green with the win, and a spot in LPGA history, in hand.
"It's just awesome watching your kid do something like this, but it is very nerve-racking, though," Scott Thompson said. "This is a very special day.
"It was an unbelievable feeling to hear people cheering your kid like that. A very proud moment."
The home-schooled teen from Coral Springs, Fla., tapped in for par, hugged her father and got a celebratory dousing of bottled water over her head from Joh.
She's still a kid having fun. She spent the evening before the tournament at Outback Steakhouse with fellow teen golfer Janie Jackson talking about boys and teenage topics.
Joh, who opened the day seven shots back, finished with a 68 after closing the gap with four straight birdies starting on No. 12. Her previous best finish was 12th at the CN Canadian Women's Open.
Meena Lee, who opened the day five shots back in second, finished with a 73 and tied with Stacy Lewis at 9 under.
Thompson closed with a tap-in for par and a drama-free finale.
She had flirted with history before. Thompson shared the 2009 Navistar LPGA lead after two rounds as a 14-year-old amateur. In May, she entered the final round at the Avnet LPGA in Mobile tied for the lead, but dropped to 19th with a closing 78.
This time, she built such a cushion that bogeys on Nos. 11 and 12 only cut her lead to five strokes over Lang and Lee. Thompson recovered with tap-ins for par on the next hole and No. 15 and coasted from there.
Thompson said the jitters never got too bad.
"I was definitely a little nervous but they were controllable," she said. "Once I hit the first tee shot I was like, 'All right, I'm good."'