Proxy appliance as an internet proxy: How DNS works?

The best place to start and understand how the Proxy works in a Virtual Lab is in the Veeam documentation here - Virtual Lab - Veeam Backup & Replication User Guide

This should help explain things.

I already followed the documentation. And from my point of view everything is configured accordingly.
However, it doesn’t work. My approach is to rule out the main cause. Does the outgoing DNS request of a VM running in the vLAB can answered by anyone else?

There was a question about something similar in the forum that you may want to check also - https://forums.veeam.com/viewtopic.php?f=2&t=99469&start=0

The Veeam Virtual Lab Proxy Appliance is neither a DNS server nor a general-purpose NAT gateway. It serves solely as an HTTP/HTTPS proxy to enable access to the Internet.
DNS resolution is not handled by the Proxy Appliance. The isolated VM must be able to contact a DNS server (for example, the internal Domain Controller or change the il primary DNS settings (8.8.8.8) for the isolated VM) that is capable of resolving Internet names, if necessary via a DNS forwarder.

I imagine you’ve entered the proxy using the IP address and the corresponding port, rather than an FQDN that needs to be resolved.

The correct flow is:
The VM makes a DNS request to its own DNS server ----> The DNS server resolves the name (locally or via an external forwarder).---->Once the IP address has been obtained, the browser sends HTTPS traffic to the Proxy Appliance, which forwards it to the Internet.

If the DNS is not working, the browser will never be able to reach websites, even if the proxy is configured correctly.

Try to check
That the VM can resolve names using `nslookup`.
That the configured DNS server is reachable from the VM.
That the browser is using the IP address and port of the Proxy Appliance configured in Virtual Lab.
That the DNS server can reach its own external DNS forwarders.

From the isolated VM, run this test

ipconfig /all
nslookup www.microsoft.com
ping <IP_Server_DNS>
telnet <IP_Proxy_Appliance> <Porta_Proxy>

or

Test-NetConnection <IP_Proxy_Appliance> -Port <Porta_Proxy>

Internal Active Directory DNS server:
   forwards unknown queries to public DNS servers
    must be reachable from the isolated VM
Public DNS server (8.8.8.8,  etc.)
 only works if the isolated network has a route/NAT allowing DNS traffic this is usually not the case in a Virtual Lab

If you could please provide the output of the commands, the configuration of the isolated VM, the proxy configuration, and the routing/NAT rules, and also check any firewall rules for the IP address on the LAN side of the virtual appliance.

According to the link posted by ​@Chris.Childerhose , Veeam Virtual Lab does not currently provide a DNS proxy or DNS forwarding service. A feature request has therefore been submitted to extend the functionality of the Proxy Appliance, enabling it to also act as a DNS forwarder for VMs within the isolated network.

It is necessary to provide the isolated VMs with a functioning DNS service (for example, an internal DNS server configured with DNS forwarding to the Internet, or a dedicated DNS server).

Veeam’s Internet Proxy alone is not sufficient, as it handles only HTTP/HTTPS traffic and does not handle DNS requests.