The relevant key for the database server is DB_CONNECTION, not DB_DRIVER:
// config/database.php
'default' => env('DB_CONNECTION', 'mysql'),
So, your .env should read
<env name="DB_CONNECTION" value="sqlite" />
Next, in the config file, there is already a default value for a SQLite database
'database' => env('DB_DATABASE', database_path('database.sqlite')),
Note that it is located within the database_path() which is {PROJECT_ROOT}/database/database.sqlite, however, you have just given database.sqlite and presumably there is not such file in the project root