Caleta-Car, a 28-year-old international from Croatia, has joined La Real on a season-long loan with the option to make the transfer permanent.
The initial loan fee is €500,000, and Lyon has the opportunity to purchase Caleta-Car's contract at the end of the season for €4 million.
Caleta-Car's deal with Lyon is set to expire in 2027, and he previously played for the French club for two years, making 57 appearances.