It is safe to open the same database from multiple processes, if POSIX advisory locks work. It is not safe to open the same database twice in the same application with separate linked copies of SQLite, if POSIX advisory locks work. By “safe”, I mean doing so won't corrupt your database. Whether your app logic handles it is a separate concern.
I don't know that there's a good solution here (though maybe just using libsqlite-dev is one), but this is a real risk of vendoring SQLite that should be considered, even if it can't be solved perfectly.