In an interview with ITV News, his stepfather said: "People wanted to meet us and show their support. He's become a figurehead to unite the country.
"We've met such good friends, incredible friends out of nowhere that took us into their homes and brought us in with their families ... It feels like [we're] part of one massive family."
Lee's mother Lyn said that people have "turned around to us and thanked us for giving the country Lee ... They've not spoken for years and years and they've brought their families back together."
She described how Lee had wanted to join the Army since he was just four: "You ask your children, 'What do you want to when you get older?' and he always said he wanted to go in the Army.
"There was never any other career he wanted to do. Always the Army was number one and he followed his dream and obviously I supported Lee's decision ..."
After serving in Afghanistan, Lyn was relieved when Lee returned to the UK and took up a post in London where she "thought he'd be safe".
"You rest up easy. They're not in the war zone and back home, doing a job that he loved doing."
Lee's sister Sara McClure said she talked Lee out of returning to Afghanistan: "He rang me not long ago. He was quite upset. He wanted to go back to Afghanistan and he was going to request a post and I talked him out of it and now I wish I hadn't."
Speaking of their enormous loss, Lyn said that a "big chunk of the calming influence and humour has gone out of the family."
"We laugh at the daft things he did. It’s what’s keeping us strong," Ian added.
Asked whether she derived any comfort from baby son Lee left behind, she said: “Jack’s all we have left now of Lee. He’s going to be one spoiled little boy.”
“You have to [keep going] for the little ones. As much as I'd love to just curl up in the corner ... You’re still a mum to them.
"You just have to get on. Put that mask on during the day and try and get through. Little steps at a time. I've never felt pain like I do now. It's there constantly, every day.”