I don’t know which one HK65 is referring to, but I know a few examples:
Punjabi, which is left-to-right in India and right-to-left in Pakistan (the Indian one being influenced by older Indian scripts and the Pakistani one by Arabic)
Kazakh uses the RtL Arabic script in the part of China where there are a lot of Kazakhs and the LtR Cyrillic script in Kazakhstan
At least some of the kinds of Tamazight (spoken by Amazigh people, mostly in Morocco and Algeria) use Arabic script, but there is a script specifically for Tamazight languages called Tifinagh which goes left to right and there’s also some use of the Latin alphabet for these languages
I know a language which kinda-sorta has two writing systems, one of which is left-to-right, the other one right-to-left.
Which one?
I don’t know which one HK65 is referring to, but I know a few examples: