Looks like you're confusing two things. When using homestead it's pretty simple.
When you start your homestead server (homestead up), the databases that are set in your Homestead.yaml file are being created. You must specify the database names in this file in order to have them available in your virtual environment. If you then create a new project your can simply use these credentials:
DB Server: localhost
DB Username: homestead
DB Password: secret
DB Name: homestead (or any other database made in Homestead.yaml)
If you want to use (php artisan migrate), make sure you've SSH'ed into your server (homestead ssh). It does not work as long as you are using the Terminal on your local machine, you must be inside homestead ssh.
On the other hand, you're talking about SQLite, in order for this to work you touch the file once so it gets created. You set your database driver to sqlite and then point the database file to the one you just touched. I haven't used SQLit so far, but I think you must also be inside homestead ssh to use the (php artisan migrate) command.
The above is basic stuff explaind in a few videos here. Sounds like you need to get back to basics to clear some things up for yourself.