The artwork is made by CrazyCookieManic
Lets get right into this one.

First hint: Starting with the fact that Luck is Charlotte's half brother. (Still only theory). Say Lucks Mother had a small thing with Charlotte's Father and got pregnant, she then left the house of Roselei leaving the mane male in need of new male heir. William was eight when his father took him back in after losing his heir, William is 26, and Luck is 18 which is 8 years apart. Meaning after Luck was taken away William was brought in.

Second hint: When William rejoins the noble family that takes him back his shown to be wearing a blue outfit, which seems to be planet base pins on his outfit. 

Third hint: William never stated what Noble family he belonged to, he simply just said "He was the illegitimate child of a certain noble." And that certain noble must have been the head male of the house Roselei. 

Fourth hint: William's World Tree Magic is a planet based magic, and the head of Roselei must also have a planet based magic.

Fifth hint: Just going a bit deeper into Luck being related to the house of Roselei, Luck has very strong magic for being a so called commoner, seems to have a lot of magic, which would make since if he where an unknown noble. And Lucks mother must not have like the head male of house Roselei and then when she left she no longer like nobles, and that's why she was so happy when Luck killed a noble.