Laravel from Scratch - Traversy YouTube - SQLSTATE[HY000] [1045] error when run PHP artisan migrate
The solution...
For MAMP users, there's a line missing from the default .env file in Laravel which basically instructs Laravel where to find mySQL:
DB_SOCKET=/Applications/MAMP/tmp/mysql/mysql.sock

You also need to change the DB_HOST and DB_PORT settings for MAMP.
This works for a default MAMP installation:
DB_CONNECTION=mysql
DB_HOST=localhost
DB_PORT=8889
DB_DATABASE=lsapp
DB_USERNAME=root
DB_PASSWORD=root
DB_SOCKET=/Applications/MAMP/tmp/mysql/mysql.sock

If you have set a username / password you should use them of course ...