During the chat, which was moderated by Katie Couric, the group remembered Natasha Richardson, who died in 2009 from a brain hemorrhage following a skiing accident. Richardson played Elizabeth James in the 1998 flick, the mother to twins Annie and Hallie (Lohan).
"Natasha had such an elegance and grace and she was so maternal to me," Lohan said.
"[She was] just somebody so giving and so glad to be there and transmitted that joy," Quaid, Richardson's onscreen ex and father of the twins, said. "It made everything that much better."
Meanwhile Hendrix, who played Quaid's much-hated onscreen girlfriend, Meredith Blake, recalled Richardson gushing over her husband, Liam Neeson, and their sons, Daniel, 23, and Micheal, 25.
"She would come into the hair and makeup trailer and she would literally swoon over talking about Liam and her kids. She would call him 'My Liam,'" Hendrix said. "And she really seemed to have it all, which to me made what happened even more heartbreaking."
The group also looked back on Lohan's casting in the film, which marked her first film role.
"Within two or three minutes, we both knew she had the part," Shyer said of him and Meyers. "She was just amazing."
"Putting aside how adorable she looked, she had that quality that just sort of leapt up at you and pulled you in. I think to be a movie star and to be the lead of a movie, you need to have that connection with the camera, that screen presence," Meyers agreed. "We discovered a big star. We discovered somebody that everybody fell in love with."
As for Lohan's onscreen dad, he had nothing but praise for the young actress.
"I had such a blast doing this movie. The first thing I remember was meeting Lindsay at some kind of screen test... I remember thinking, 'Oh my gosh. This is one of the most talented people I've ever met. Period. Forget that she's 11 years old,'" Quaid, 66, said. "I actually thought that there were two girls. I really did because your accent was so perfect... You were a natural. You just fell right into it."
When it came to Lohan, she couldn't think of a better first project to be involved in.
"I was so young and it was just so fresh for me. It was my first movie audition, my first screen test, my first time in front of people like Nancy and Charles and on a sound stage. So I was just, like, a kid... I was really excited," Lohan, 34, said. "I didn't feel like I was working. It just felt like a really incredible learning experience for me and a lot of fun."
Lohan also recalled how she managed to play two characters during the project, revealing that her time in the hair and makeup trailer made a world of difference.
"Once the long hair was on, it felt very different for me... Once you put a wig on someone, you feel different. You're stepping out of your comfort zone and you kind of become the other character," she said. "I feel like people almost treated me differently when I was Annie, because Annie was so much nicer and Hallie was kind of like me."
The whole experience had both an immediate and long-term impact on Lohan as a person and an actress.
"My parents were kind of separating at the time when this was all going on and it made it a lot easier for me to play these characters that were figuring it out. I felt so lucky and really blessed by Nancy and Charles," she said. "Without this movie, without this, I wouldn't have gotten that acting bug."
"How do you not only want to act for the rest of your life after doing a film like this with such great actors? The Parent Trap, it's beautiful, it's timeless, and it's special. It's just really special," she added. "I just feel really blessed and really grateful to have been a part of it."
"When it comes down to it, this movie just had some sort of stardust that was just sprinkled on it," Quaid agreed. "It just happened in the ether."