In the new Pokemon Anime, you may have seen people and articles differentiate between the two spellings. The reason being, unlike Ash's being name being completely different from his name in the Japanese Version, they plan on keeping the original names for the new protagonists in international versions. Such, they had to translate the Kana to English. Let's start with Roy.
Roy's name in Japanese is ロイ . When translated from Kana to Roman letters, it's widely accepted for it to be spelt as "Roi", as ロ is "ro", and イ is "i". This is why a lot of fans spell his name as Roi; it isn't incorrect! However, his name is still spelt as how English speakers pronounce "Roy", which is probably why they made the change.
Liko's name in Japanese is リコ. When translated from Kana to Roman letters, it's widely accepted for it to be spelt as "Riko". Unlike Roy's name, there's a bit of a difference here. リ is usually spelt as "Ri" (see below), and コ is "ko".
Due to a handful of complex reasons that can usually be simmered down to "there's no difference between L and R in Japanese", It can also be translated to "Li". Although most commonly being accepted as an R, the "R's" of Japanese sound like a mixture of R and L, but also not at the same time, which is where that came from in the first place. Either way, "R" can be argued as "more correct" spelling over L (see Japanese keyboards and romanized lyrics to Japanese songs), but the "L" isn't incorrect either.
Her name may be chosen as "Liko" for the dub version due to it sounding and looking more English.
TL;DR: Roi/Roy and Liko/Riko are both correct, it's a matter of localization while translating.
