I just did this today successfully. I have a Synology ds213j.

You need to create a virtual host entry in Synology webstation. Control Panel -> Web Services -> Virtual Host button -> Create button

Subfolder for entry needs to be /public/ and Synology allows only one directory down... in other words you must have your Laravel project in the root www directory on Synology then add the entry with "public" as the subfolder. You must also pick a host adress (e.g. "mysite.com")

Be sure to point your local machine to the correct IP address by configuring the hosts file.

on linux: sudo nano /etc/hosts then add line like: 192.168.1.123 mysite.com

on windows you need to run notepad as admin and edit your hosts file with same entry.