Is it possible to configure Sonicwall TZ350 to provide DNS for DHCP clients?

I've got a SonicWall TZ350, and I've set it up to provide DHCP to a local LAN (192.168.168.X). Right now, when a DHCP client on the local lan does nslookup of another client, it fails because the name server that the SonicWall is providing is the name server passed through from the WAN.

Is there a way to get the SonicWall to ack as a DNS server for the DHCP clients? I would like the SonicWall to offer itself as DNS server, and answer for any DHCP clients, but forward anything else to the WAN DNS server (similar to how it works in pfSense when you use the DNS Forwarder option with 'Register DHCP Leases in DNS Forwarder).

Is this simply not a thing that the SonicWALL does? I certainly can implement my own DNS server/DHCP server on the LAN (pfSense), but it seems like a natural thing for the SonicWall to do, so I tend to think I just don't know what I'm doing here.

No, SonicWall does not act as a real DNS server. If you have a tiny network, you could enable DNS Proxy on the SonicWall and fill out the cache by hand for your local domain. Anything more than that and you'll have to setup a local DNS server.