The Harry Potter movies made many big changes from J.K. Rowling's novels, including the ages of Lily and James Potter. In the books, Lily and James are only 21 years old when they died, which is confirmed in the films by the dates on their gravestone shown in Harry Potter and the Deathly Hallows Part I. However, Lily is played by Geraldine Somerville, who was 34 when the movies started and 44 when the movies ended, and Adrian Rawlins, who played James, was even older, 43, when the movies started and 53 when they ended.
Harry's (Daniel Radcliffe) dead parents appear a few times throughout the eight-film Harry Potter franchise, most notably when they visit Harry before he goes to die in Harry Potter and the Deathly Hallows Part II, called forth with the resurrection stone. Originally classmates of other important characters like Severus Snape, Sirius Black, Remus Lupin, and Peter Pettigrew at Hogwarts, James was killed outright by Voldemort, and Lily sacrificed herself to protect the infant Harry before the beginning of the franchise's main action.
Casting James and Lily as older actors in the Harry Potter movies likely fit better with the other actors cast in adult roles and made sense when they actually appeared as Harry’s parents. Of all the actors cast in the Harry Potter series, Snape is arguably the most iconic. Casting Alan Rickman, picked specifically by JK Rowling, had ripple effects across the rest of the adult cast in the movie. He was 55 when the movies started, while Snape in the books is 31 at the start of Harry’s first year. While some of that difference could be handwaved – he’s living the hard life of being Dumbledore’s double agent with Voldemort, after all – the other actors cast had to be believable as Snape's contemporaries. Casting Gary Oldman (43 at the start of the movies), David Thewlis (38), and Timothy Spall (44) as Sirius Black, Remus Lupin, and Peter Pettigrew makes sense through this lens.
The other reason Lily and James are older is that they have to look like Harry’s parents. They first appear to Harry in the Mirror of Erised in Harry Potter and the Sorcerer's Stone, when he’s 11 years old. Casting actors in their early 20s would look strange in that role, standing next to their 11-year old son, so older actors were cast. Since fans didn’t even have James and Lily’s ages confirmed at that time until the final book was released 6 years later, there was no reason not to cast older actors.
James and Lily's different ages are never explicitly acknowledged in the Harry Potter movies - their gravestone still shows them dying at 21 - and unlike other changes, this didn’t draw as much attention from the fans, as it worked out all for the best. Making them older looks right and helped make other casting, especially Alan Rickman, make sense where it otherwise might not have.
