Can you use telnet <remote ip> 8443 from the remote host and check you can actually connect to the remote port, it may be there is a firewall blocking access.
So I’m assuming that lxd1 is the 192.168.1.10 address. Is there anything in the syslogs for that server indicating any problems, as it suggests the request is timing out.
root@lxd1:~# ip r
default via 192.168.1.211 dev eno1np0 proto static
192.168.1.0/24 dev eno1np0 proto kernel scope link src 192.168.1.10
root@lxd:~# ip r
default via 192.168.1.211 dev eno1 proto static
10.63.26.0/24 dev lxdbr0 proto kernel scope link src 10.63.26.1 linkdown
192.168.1.0/24 dev eno1 proto kernel scope link src 192.168.1.11
root@lxd1:~# ip r
default via 192.168.1.211 dev eno1np0 proto static
192.168.1.0/24 dev eno1np0 proto kernel scope link src 192.168.1.10
root@lxd:~# ip r
default via 192.168.1.211 dev eno1 proto static
10.63.26.0/24 dev lxdbr0 proto kernel scope link src 10.63.26.1 linkdown
192.168.1.0/24 dev eno1 proto kernel scope link src 192.168.1.11
Please can you verify that you can add a remote from the local subnet to confirm its not an issue with LXD, but an issue with the way your proxy is working. Thanks