I used this SQL:
CREATE TABLE NewEmployees(EmployeeID INTEGER PRIMARY KEY AUTOINCREMENT, LastName TEXT, FirstName TEXT);
and using SQLite3.exe did this
SQLite3 employees.db .read create.sql .exit
which created my database but no tools nor the SQLite.NET provider can read it, I get the error "malformed database schema near AUTOINCREMENT?
That really sounds as if the tools and the provider are using a pre-3.1 version of SQLite, since AUTOINCREMENT wasn't introduced until 3.1.0.