There was a study of Chinese kids learning English, and only 1/4 or 1/3 of kids who were dyslexic in one language were dyslexic in the other one too. I don't have the link to hand but can probably dig it out if someone is interested.

There's also the famous case study of Alex, who was dyslexic in English but an excellent reader in Japanese.

So my uneducated understanding is that "dyslexia" has to be a cover term for multiple issues. Difficulty matching characters to sounds might make for a below-average reader in Chinese, and difficulty recognizing characters might make for a below-average reader in English, but reverse the languages and both kids would be dyslexic. On the other hand, there are those 1/4 to 1/3 of kids who are bi-dyslexic which suggests there may be some global mechanism accounting for some dyslexia.

P.S. The most recent trendy thing I know about is the "crowding" explanation for dyslexia, which hypothesizes that dyslexia really is a vision problem, but the problem isn't mirroring but rather difficulty separating characters at normal spacing. This only appears to hold true for a subset of dyslexics, and that particular study totally failed to distinguish between the effects of increased spacing between characters, increased spacing between words, and increased spacing between lines. This study of Italian dyslexics found that increasing spacing between characters without also increasing spacing between words is worse than nothing, a condition that wasn't tested in the study above.

I'd like to see a test of increased line spacing only. I remember that increasing line spacing was (and is) helpful when reading a script that I read slowly and poorly because when reading what were very long lines for me but normal for natives I'd lose track and my eyes would wander onto adjacent lines.

Edit: The English study I linked to showing spacing greatly helping a small group of dyslexics drastically helped with reading "pseudowords", a common test of ability to sound out words. It helped much less with real words. So it's interesting that the Italian study showed no useful effect, because Italian spelling is much simpler than English spelling and so you'd expect Italian readers to rely much more on sounding out words.