Hello,
You could try to add this to the "Lansweeperservice.exe.config" file :
<system.net>
<defaultProxy useDefaultCredentials="true">
<proxy
autoDetect="false"
proxyaddress="http://192.168.1.10:3128"
bypassonlocal="false"
usesystemdefault="true"
/>
</defaultProxy>
</system.net>
I didn't tested myself because I don't use cloud relay but it works for many .net software.
Don't forget that if your proxy need authentication, the service account will be used.