Your terminology is making it hard to give advice.
I think you mean "firewall" by "Gatekeeper" and "some server on the LAN with the 'my_computer' machine" by "master_server". You mention in a comment "I have no control over gatekeeper and probably none over master_server as well." That makes me think that you're not the systems administrator for this network, which limits your options.
Most IPv4 local area networks (LANs) that are connected to the Internet today use a firewall, located at the border of the LAN and the Internet connection. This device performs Network Address Translation (NAT), translating network traffic between private IP addresses (taken from RFC1918) used on the LAN into one or more public IP addresses assigned by the Internet Service Provider (ISP).
Here's what would typically happen when accessing your website from a device outside the LAN (e.g. your "smartphone"):
A systems administrator would typically configure the firewall to accept incoming connections from the public Internet
Your smartphone would make a request to one of the public IP addresses assigned to the Internet-side interface of the firewall
The firewall would receive the request from your smartphone and translate the "destination" address from the public IP address to the private IP address assigned to the "my_computer" host
The firewall would place the translated request onto the LAN
The "my_computer" host would receive the connection request from the Internet and respond back, via the firewall.
The firewall would receive the response from the "my_computer" host and translate the source address back to the public IP address the smartphone's request was originally sent to
The firewall would send the translated response to the ISP's router
Since you don't have control of the firewall you can't do what would conventionally be done.
There are other options, but none of them are as good as contacting your systems administrator and having the right forwarding through the firewall configured.