The brothers, aged 12 and 10 respectively, are both goalkeepers and had been part of Real Madrid's La Fábrica youth system after beginning their footballing journeys at Pozuelo.
Their move to Leganes follows a decision made by the boys and their families, with the new club viewed as offering a more suitable environment for their development.
Both youngsters had made an impression in youth competitions during their time at Madrid.
Martín attracted attention at the Brunete Under-12 World Cup, while Lucas produced a particularly notable performance in a penalty shootout against Barcelona, saving several spot-kicks.
The brothers now begin a new chapter at Leganés, leaving behind the club where their father became one of the most celebrated goalkeepers in Real Madrid's history.
Casillas made more than 700 appearances for the senior side, winning multiple domestic and European honours, and remains closely associated with the club.
However, the decision to move his sons reflects the importance of finding the right sporting environment for young players, rather than simply following the most prestigious academy pathway.