LightBurn itself does support proxy servers, but not scripts - there is a "Use Proxy Server" setting in the License menu.
The proxy format is:
[protocol://][username:password@]machine[:port]


Examples of valid proxy strings:

http://127.0.0.1:8000/
http://user:pass@127.0.0.1:8000/
socks5://127.0.0.1:8000/