Could you explain how to create a Linux virtual server to use Laravel on the WEB ?

You need to install a webserver software (Probably apache) on linuxof your choice, an then on the server you need to setup Virtual Host, and publish your files.

https://www.digitalocean.com/community/tutorials/how-to-set-up-apache-virtual-hosts-on-ubuntu-14-04-lts

Maybe consider Laravel Forge -- it's the real thing for Laravel deployments on professional hosting services (including Digital Ocean, EC2, Rackspace, etc).  Good "learning links" here:
https://laracasts.com/series/server-management-with-forge
https://scotch.io/tutorials/deploy-php-apps-easily-with-laravel-forge
https://www.sitepoint.com/setting-up-php-7-servers-with-laravel-forge-and-digitalocean/
https://mattstauffer.co/blog/getting-your-first-site-up-and-running-in-laravel-forge

Hi

I'm a little confused.

I tought Laravel app works like a Codeigniter app f.e. in terms of instalation, nothing special must be done if compared at a pure PHP code running on server - just install the framework (*).

You are suggesting to contract a provider to install  Laravel  making it  possible to run . Isn't it?

I still have a provider that trusted me Laravel site can run on it... (I didn't asked any other detail him due to (*))

Could you please clear these points?

And plus...  it seens a Laravel app couldn't cohexist with an existing Codeigniter that remains in another folder. Isn't it?

Thank you William

Much clearer now.
Now it's up to me to get the concepts meaninng apurated, to make more sense, gradually.

You will need to buy a server for that and setup Linux environment on it. If you don't have sysadmin skills to setup your own server, then you can host Laravel on a Linux based server using Cloudways. This Laravel web hosting platform lets you deploy Laravel on a server in just one-click. This means there is no need to manually setup OS and configure stack. Just launch the server and start building.