As Elsa and Lucius/Frozone are from different series, they have never met in canon. As well as the fact that Frozone is also a Pixar character. Even though a few Disney crossover video games could have them cross paths with each other or get them added in the same team, by the player's choice.
Both Elsa and Frozone use ice-related powers, and have used their abilities to run across large bodies of water. They use their powers to keep innocent people safe from villains and to bring the magical joys of winter, even though a few of them were the main reason why Elsa and Lucius were forced to hide their ice abilities. The two also wear blue colored clothing, that are seen as their signature outfits. Just as "Frozone" is Lucius's superhero title, the title of Elsa's Disney film is "Frozen". Frozone comes from a world of superheroes, while Frozen II has Elsa entering a world of magical beings.
Elsa and Frozone are two of the main members in the Secret of the Incredible Frozen Guardians crossover fandom, with Jack Frost from Rise of the Guardians and Periwinkle from Disney's Fairies. As well as them being apart of the expanded ice character fandom, Just-Ice League, where Mr. Freeze from DC Comics, Iceman and Loki from the Marvel universe, The Ice King from Adventure Time and Jack are all seen as Frozone's love rivals for Elsa's affections.
While the ship itself isn't very popular as some of the other ice character crossover ships involving Elsa or Lucius, it still has a few loyal fans that like the idea of using their icy trait as a reason to ship them together as lovers or friends. Even though their ice power and blue signer colored clothing is two of the main things that they have in common, along with their Disney films having something to do with family. Despite The Incredibles only having Lucius as an uncle-like figure to the Parr family, while Frozen is mainly of the sister bond that Elsa shares with Anna.
In some Superhero AUs of The Incredibles universe, Elsa is commonly seen as Frozone while he is portrayed as her or is placed in Elsa's blue dress, for fun, in a Frozen AU. While Frozone wasn't one of the Disney cameo characters to be seen in Ralph Breaks the Internet, fans could have the canon netizen of Elsa meeting a fanon netizen version of Frozone in fanfics and art.
- Both are two of the playable characters in the Disney crossover games, Disney INFINITY, Disney Emoji Blitz, Disney Magic Kingdoms and Disney Heroes: Battle Mode.