LwIP version 2.03 also have support for mDNS. I tried to implement it using the latest STM32CubeMx for the F7, and it does not enable mDNS also .
I tested it in a MIMXRT1021 board from NXP, and there are an example of http server with mDNS, and it works well. I noticed that it depends on setting the ethernet MAC to multicast address 01 00 5E XX XX XX. I don't know how to do it on the STM32H7.
In case someone else struggles with this, note that LWIP_MULTICAST_TX_OPTIONS is enabled or disabled as an Advanced option within the Key Options tab.
Ergo, one must tap 'Key Options', select 'Show Advanced Parameters', and look for 'LWIP_MULTICAST_TX_OPTIONS' within the 'IPv4 - Multicast Options' tree item to enable or disable this option.
If the option is disabled, you may not be able to enable LWIP_IGMP, and that may prevent you from enabling LWIP_MDNS.