[radus]

Not a Supabase user, but to my knowledge -- no. Except for a set of blessed extentions, Supabase only supports extensions that are written in "trusted languages" (ie. supported by pg_tle), and Lantern is written in C, which is currently not supported.

[diqi]

pgvector is written in C and is supported by Supabase. There's nothing inherent preventing Supabase from supporting Lantern.