The pair sat down for an interview for BBC Sport in the grounds of Prince William and Kate's London residence, where the Duke presented Lauren with a personalised cake to mark her 27th birthday.
WATCH: Prince William surprises Team GB's Lauren Price with birthday cake
The fondant-covered cake was in the shape of a boxing ring and featured two red marzipan boxing gloves. Its message read: "Happy 27th Birthday Lauren + Good Luck!"
As William placed the sweet treat on the table, he smiled and said: "I hope it tastes alright but you can take it home with you, you don't have to eat it all now!"
He added: "Happy Birthday for today and hope you have a good day. We'll all be wishing you well, Lauren, and cheering you on. You'll do us very proud in the Olympics, I'm sure, and you'll do everyone proud in your hometown, and your grandparents as well, so best of luck!"
Prince William surprised Lauren with a personalised cake
Lauren, from Ystrad Mynach, will become Wales' first female boxer to compete at the Olympics this summer. She won kickboxing world titles as a teenager and played international football for Wales before switching to boxing in 2014.
In 2019, she won gold at the World Championships and European Games, and is also the reigning Commonwealth Games champion and ranked world number one.
Lauren spoke about her early boxing career when she had to balance training with her job as a taxi driver, and how competing at the Olympics has been a lifelong dream of hers: "It's been a dream of mine since I was eight to go to the Olympic Games. I remember being sat in the living room with my Nan and Grandad watching the Olympics and seeing Kelly Holmes win gold, and at the time I didn't know what sport I wanted to do, I just wanted to go to the Olympic Games."
Lauren was raised by her grandparents, Derek and Linda Price. Sadly, Derek passed away last November.
William invited Lauren to Kensington Palace
When William asked Lauren how her grandmother will support her while she's away in Tokyo for the Games, she revealed that her Nan sends her inspirational text messages, adding: "She'll remind me how hard I've worked over the years and how much my dreams mean to me. She always used to say to me 'reach for the moon, if I fall short, I'll land on the stars' and that's something that's always stuck with me."
Speaking in a clip, Lauren's grandmother, Linda, said: "It's just sad that her grandfather is not here to see it, because he would have been the proudest man in the Valley."
Lauren then told William: "It's something I take with me in the ring, I know he's always looking down on me."
Watch the full chat between the Duke of Cambridge and Lauren Price on BBC Sport's website now.
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