I am using sqlite3 in a linux machine and I am getting the database without username and password. Can I set a username and password for the same?
No, sqlite3 databases are very lightweight systems. They need no server and all data is stored in one file. A username/password is not supported by the sqlite/sqlite3 package.
In order to achieve simplicity, SQLite has had to sacrifice other characteristics that some people find useful, such as high concurrency, fine-grained access control, a rich set of built-in functions, stored procedures, esoteric SQL language features, XML and/or Java extensions, tera- or peta-byte scalability, and so forth.
However, since it's only a file you can encrypt the file with a password to protect your data.
SQLite is mainly an embedded database engine, not intended to be used as a multi-user database server that would require usernames and passwords.
You can always encrypt the database file with some user-provided password/-phrase, I guess. But expecting an embedded DBMS to sport full-blown access control is too much.