Problem
If you have a IETF language tag like lzh the only way to figure out that the Wikimedia language code for that language is to query the siteinfo of every site in the matrix and get the lang attribute. Doing this would inform you that zh-classical is the wikimedia language code.
Solution
Add the lang (from the siteinfo) for each wiki to the SiteMatrix API. This could also be added to the special page (just for "other"?) to resolve T167825