I always like to tie all the canons together: Klonoa was born in Lunatea and grew up there like in Heroes, but as the Dream Traveler he can never stay in either Lunatea or Phantomile forever. He will always eventually "wake up" and will always eventually "fall asleep", which is why he moves from Phantomile to Lunatea to the Empire of Jillius (which I think is a part of Phantomile we never visited in the first game, similarly to how heroes has places in Lunatea we didn't visit in LV) back to Lunatea (as dream champ takes place somewhere in the empire, according to the game manual). He always moves between these worlds back and forth.
Additionally, he seems to be able to travel between these states of being while "asleep" or while "awake". When he sleeps he doesn't seem to physically leave one plane of existence for another, we know this because he doesn't disappear when he sleeps during idle animation in the GBA games (but his state of dreaming still allows him to move between dreams), however, when he's awake and traveling between worlds and dreams we see him physically leave one world for another, like in the end of DTP and LV
I made a terrible video about this, but I feel the need to explain every time I delve into something relating to this because even I can't watch that video without cringing at how I sound and how poorly I explain things... Hopefully sleep deprived me did a better job or some halfway decent job. Onto the story:
During his childhood he is, because of him being the Dream Traveler, summoned by Huepow to help save Phantomile. Because he was awake while this happened, he physically was taken his home in Lunatea (maybe this is part of the reason why Grandpa is so protective of Klonoa in heroes??) to be brought to Phantomile, a place completely alien to him. And I think Huepow realized that being taken from your friends and family and home to beat up some baddies wasn't going to make this person want to save the world, so he fabricated memories to make Phantomile seem like his home, so he'd want to fight to defend it. This wasn't hard morally for Huepow to do because at the time Klonoa was a stranger and his home was in danger, and I think after the events of DTP Klonoa might have been upset with Huepow for a while but starts to understand the weight of the situation they were all in...
And because Klonoa's memories were warped by Huepow (and he was forcibly taken from Phantomile before he could undo it), and because Lunatean's rejected sadness before Klonoa came to save the day again (and why wouldn't your friend being virtually kidnapped be a sad memory? Of course it would end up suppressed in their minds) Klonoa doesn't remember Lunatea, and his friends don't remember him, until everything is balanced again.
Of course, as time goes on and Klonoa learns more and more of what it means to be the dream traveler, he gets to go back and forth between worlds and isn't separated from his friends in either worlds forever <
Sorry I know this is terribly written I need a nap