Hi @lorenzo,
I'm using fairly similar set up. The simple answer is you have to set it up on your live server the same way you were setting it up on your local machine so as per your guide http://laradock.io/guides/#Digital-Ocean:
Install docker first:
Install Docker
Visit DigitalOcean and login.
Click the Create Droplet button.
Open the One-click apps tab.
Select Docker with your preferred version.
Continue creating the droplet as you normally would.
If needed, check your e-mail for the droplet root password.
Install laradock with all of the image docker configurations:
$root@server:~# apt-get install git
$root@server:~# git clone https://github.com/laravel/laravel
$root@server:~# cd laravel
$root@server:~/laravel/ git submodule add https://github.com/Laradock/laradock.git
$root@server:~/laravel/ cd laradock
Once you have both then you tell docker to pull in all of the images
$root@server:~/laravel/laradock# curl -L https://github.com/docker/compose/releases/download/1.8.0/run.sh > /usr/local/bin/docker-compose
$root@server:~/chmod +x /usr/local/bin/docker-compose
Once images are downloaded then you create the containers that you need:
$root@server:~/laravel/laradock# docker-compose up -d nginx mysql
Once that is ready to go, you enter your workspace container and pull in the Laravel:
docker-compose exec workspace bash
$ root@workspace:/var/www# composer install
$ root@workspace:/var/www# cp .env.example .env
$ root@workspace:/var/www# php artisan key:generate
$ root@workspace:/var/www# exit
$root@server:~/laravel/laradock# cd ..
$root@server:~/laravel# sudo chmod -R 777 storage bootstrap/cache
And then once you set up all your nginx, dns etc to point to the correct folder for instance:
root /var/www/public
You install another git in that folder and pull your private repository with your project that you commited from your local machine to github, bitbucket etc.
After you set it up then the only thing you will be doing is:
On you local machine:
git add .
git commmit -m 'My another commit'
git push
On your Digital Ocean:
git pull
Here is Jeffrey lesson on git:
https://laracasts.com/series/git-me-some-version-control
I hope it helps!