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I could not care less about if Green and Leaf are the same character, but it is clear that Lyra and Kris are different. The vast majority of Johto characters look almost the same, with the exception being the Rocket executives, whose males shared the same sprite.
However, Lyra is an exception. This is most apparent when seeing her depiction in the manga. While the manga is not canon, this art difference should be very apparent.
Moreover, they have different official names. Lyra was refered to as such in HGSS content, while Kris was called that on the back of Crystal. Also, Lyra made an appearance in the Ashnime as a character, while Marina, Kris's counterpart in "The Legend of Thunder" episodes, appeared as a separate character on a magazine. Finally, there is the obvious point that they are separate characters in Masters.
While the major character redesigns in ORAS may seem like as easy rebuttal, that game had radical changes for all characters, not just one. Furthermore, ORAS and HGSS were released years apart, with design philosophies changing between their releases.
In short, Kris and Lyra are separate characters.
