This is confusingly worded but for onlookers: sqlite as you think of it isn't an application at all, it's a C library. There does exist a binary called sqlite3 which is an interface to that library, and that binary is (mostly, though not exclusively) single-threaded.
But unless you're using that specific tool, and you're probably not unless you yourself are typing "sqlite3" into a bash shell, you're using the library rather than this query tool. And that library interacts in a similar way to a socket connect or a fopen call. You can have multiple connections open to the same sqlite database, and those connections can operate concurrently (subject to various limitations, but "you need better single core box" is not the summary)
But unless you're using that specific tool, and you're probably not unless you yourself are typing "sqlite3" into a bash shell, you're using the library rather than this query tool. And that library interacts in a similar way to a socket connect or a fopen call. You can have multiple connections open to the same sqlite database, and those connections can operate concurrently (subject to various limitations, but "you need better single core box" is not the summary)