In WAL mode you can write from multiple threads without any problem, but you need to keep serializability in mind. Specifically, no concurrent write transactions are allowed. In other words, you can't have a transaction start at X, have another transaction start at X+1, issue DML and commit, and expect your original transaction from X being able to commit - it will never be able to.

Some SQLite wrappers (notably, Python's) mess with the start and rollbacks of transactions and make this appear buggy.