So far, all the mascot legendaries have been partially related to a previous group:
Gen II: Ho-Oh and Lugia, their secondary types were gained from Winged Mirages, whereas Lugia's primary type is unrelated to their theme.
Gen III: Unrelated. Suicune shares Kyogre's type, however.
Gen IV: Dialga, Palkia and Giratina have Latias/Latios' primary typing as their secondary one.
Gen V: Tao Trio does the same as above, but also has Legendary Birds' typing.
Gen VI: Unrelated.
Gen VII: Nebula trio largely shares Creaton Trio's types and Pixies' Psychic.
My personal guess is:
Gen 8: Fire/Psychic, Water/Psychic and Electric/Psychic
Gen 9: Fairy, Steel/Flying, Dragon/Fighting
Gen 10: Fighting/Ground, Fighting/Water & Fighting//Flying
Gen 11: Ice/Fighting, Rock/Fighting & Steel/Fighting
Gen 14: Fighting/Flying, Psychic, Dragon/Dark
Gen 15: Ghost/Dark, Ghost/Fairy, Ghost/Dragon
Gen 16: Grass/Ghost, Rock/Ghost, Steel/Ghost
Gen 17: Ground, Fire, Rock/Dragon