I'm assuming you have checked nothing else is using port 80 (which I assume lighttpd is configured to use). Check that bonescript still doesn't have the port bound, stop it with:

systemctl stop bonescript.service
systemctl stop bonescript.socket

I wrote a simple script for systemd to call …

… which was the source of the problem. Your "simple script" overrode where the standard output and standard error were sent. And that entirely unnecessarily. All of the redirection, PID file writing, nohup-ing, and forking is entirely unnecessary for something that is already daemonized and already has its PID known by the service manager. You don't need any part of that script at all. Instead, write your service unit like this:

[Unit]
Description=Start my_program client after system is booted

[Service]
Type=simple
ExecStart=/home/frederick/Applications/my_program-go/my_program-local -c /home/frederick/Applications/my_program-go/config.json
WorkingDirectory=/home/frederick/Applications/my_program-go/
StandardOutput=journal+console

[Install]
WantedBy=multi-user.target

Invoke whatever options are necessary to stop your program from forking, unless it actually definitely implements the forking readiness protocol. Very few programs actually do. Your "simple script" certainly didn't, as it exited the parent process long before the dæmon had initialized and was ready.

Further reading

• Jonathan de Boyne Pollard (2015). The systemd house of horror. Frequently Given Answers.
• Systemd kills service immediately after start
• Yocto linux service script problem
• The systemd.exec man page (and also systemd.service and systemd.unit). The man page says: Unit configuration files for services, sockets, mount points, and swap devices share a subset of configuration options which define the execution environment of spawned processes. This man page lists the configuration options shared by these four unit types.