The LXD proxy is a network connection proxy, and not a SOCKS5 proxy. Therefore,
it will link up the container with the host at the specified port, and there is no authentication possible.
To answer your question, you would need to get curl to specify properly the username/password of your actual SOCKS5 proxy.
With curl, you specify those as follows:
If you have a Web server or other network service that does not require access to the Internet.
That could be a Web server, either static, or dynamic like WordPress, where you install mysql/mariadb in the same container.
You want to examine software (as in forensics) or create a honeypot and you decide not to go for a VM. For the former, you use software like mitmproxy.
You want to give legitimate SSH access for some specific work that is limited within a container. But you want to be on the safe side if their credentials are compromised.