My guess: Phantomile and Lunatea are not real, and, in reality, the events of the games are Klonoa's dreams.
Think about it, the theme of dreaming is present in every game, and Phantomile and Lunatea are considered dream worlds Klonoa has to inevitably "wake up" from. In fact, having to wake up from Phantomile was the reason Klonoa was forced to leave that world at the end of the first game. This could very well be him having to wake up from a dream and back to the real world.
This would explain his fake memories: in a dream, you don't exactly have any recollection of the real world. It would even justify the inconsistencies we see throughout the games: for example, Phantomile and Lunatea are established to be different worlds and yet we see regions from both in Klonoa Heroes (which only takes place in one world). Also, when you finish Klonoa 2, you get a "good morning" message, implying Klonoa has once again woken from another dream.
So there you have it: this theory would explain his fake memories, the main theme of the games, him having to inevitably leave the dream worlds, the inconsistencies we see throughout the franchise and to top things off, it's not even a theory anymore since Dream Traveler of Noctis Sol confirmed it: in that comic, Klonoa not only refers to the events of the games as "his dreams", but he also enters Phantomile by going to sleep. Interestingly, he is shown to also be a cat/bunny in real life.
I will admit, I'm not 100 percent sure if this is the official view, but it's the one I like to have. Also, it would make Klonoa one of the few if not the only piece of entertainment to have a good use of the "it was all a dream" plot twist.