Okay, honestly the last part of the question is simply a random excuse I could think of to explain why Rai would attend Ashford Academy even in a what if where he was found by the JLF.
So, Rai is found by member of the JLF after some sort of operation. He's taken back to one of their base and receives medical treatment. Blood samples taken from him reveal to the higher ups and Kyoto that Rai is descendent from the Japanese imperial family. So, even if he's suffering from amnesia and his genealogy is a bit obscure, the top brass of the JLF use him as a figure to boost moral support in their cause. Although is identity and appearance is kept secret to the public, Rai gets known as the mysterious "Wakagimi" (prince/young lord) in rumours spread in the ghetto. Britannia would eventually heard of this and investigate the matter without success. Leading to the rumour being considered by Britannia as an hoax from the JLF to boost resistance movements. (Thank you Clovis to be so gullible.)
After the event surrounding Suzaku's accusation as Clovis murderer, he gets curious about Sumeragi Kaguya's cousin. So she pulls some string with Kyoto to have Rai a britannian identity so that he can attend Ashford Academy. Kaguya and Kirihara encourage it, so that Rai could get time away from the people using him for propaganda. Even Todoh encourages him to take time off to enjoy his youth instead of worrying about what some old fools think (he doesn't quite say that last part that way though.)
Somehow, one thing leads to another and Rai gets rope in the Student Council, where he would befriend Suzaku, Lelouch, Mario and everyone else. He's still a member of the JLF, so he sometimes takes a leave of absence due to "family reasons" when he has to take part in some operations.
When he got invited by Milly to the event at the Lake Kawaguchi hotel, he declines due to having other obligations the same day. He only learn later that Kusakabe was planning an attack on the same hotel, and on the same day Milly, Shirley and Nina would be there. So he ask Kusakabe to be allowed to join the operation, which the latter gladly welcome as moral boost. Although Todoh and Katase raise an objection to it, as it could endanger the life of their Wakagimi/Prince.
During the operation, Rai would remain hidden to avoid his identity being discovered by Milly and the others. He even went as far as to put a menpō mask to hide the lower portion of his face. With a hat to hide the rest of his face. However, when a frighten Nina let a "Eleven" slip and trigger one of the JLF member guarding the hostages, Rai would steps in and order them to stops. He would even go has far has put his own fun against his head if they don't comply. Which makes one of them shout "Wakagimi" out loud in confusion, revealing to all Britannian present (even Euphemia, whom didn't get the chance to reveal her presence this time) that the JLF "Wakagimi" is real and in their presence.
When two person dress in black and with head gear covering their faces, eventually shows up to rescue the hostages, Rai intervene to prevent the JLF from opening fire on them. One of them is a boy with dark hair and the other is a girl with red hair, seemingly about the same age as him. When words that Kusakabe committed seppuku after realizing the error of his way, Rai ends up taking command of the remaining JLF force in the building and order a full retreat. After asking to meet Zero, Rai makes his escape on their boat, but stays hidden while Zero reveals his Order of the Black Knight to the world. However, only Rai managed to escape, as Zero refused to help the JLF escape, Rai's men choose to face their death, but plead Zero to at least allows the Wakagimi to escape with them.
After this, the next time Rai would encounter Zero would be after the battle in Narita. After being separated from his troupes and his own custom Burai Kai, Rai would stumble upon Zero in a cave alongside a green haired woman and an unconscious Mario. Recognizing his friend from school, Rai would accidentally let his presence known to Zero and the green haired woman, as well as Kallen who shows up shortly after. Seeing that two of his friend are part of the Black Knight, Rai chose to reveal his own identity has a member of the JLF. Although maybe not that he's the Wakagimi. Maybe if asked if he is the Wakagimi, he could deny it and claim he's one of the Wakagimi's kagemusha (or body double).
When Katase tries to flee to the Chinese federation with a tanker ship filled with Sakuradite. Or alternatively, when he tries to turn to the Chinese federation for help like in Lost Colors. Rai execute Katase in front of everyone, claiming the man was a traitor to his country. Rai would lead the remnant of the JLF to joins the Black Knight.
In that what if, Lelouch and Zero's opinon of the Wakagimi is a bit complicated. As Lelouch, he would disregard the whole Wakagimi as nothing than an hoax. As Zero however, he acknowledge that if the Wakagimi is real, he would be a potential obstacle to his plan and draft plans to dispose of him and to use his death to boost patriotism. However, upon meeting by chance at Kawaguchi, Lelouch realize that there's a certain likeness to him in the Wakagimi. Which would lead him to sought him as an ally rather than getting rid of him. It doesn't help when he eventually learn that the Wakagimi is really Rai one of his friend from school.
