I don’t think there’s a QuickSet mode that would fit your needs completely.
The quickest way of configuring would be the following (based on default Home AP config):
start off without connection to the rest of your network. Tape WAN ethernet port (ether1), it won’t be usable in your case
connect management computer using one ether2-ether4 and use GUI of choice to conect to 192.168.88.1 (default IP address of device), you can do it using web interface. Be sure to use “normal” GUI mode (in case of web interface that’s Webfig) and not QuickSet
in IP → DHCP server disable DHCP server
in IP → DHCP client add new client, use “bridge” interface
in Wireless configure (change from defaults) wifi settings (SSID, preshared key, …)
connect one of ether2-ether4 ports to your D-Link
in IP → Addresses verify that hAP lite received IP address belonging to the rest of your LAN. If it did, try to connect to its IP address from a “normal” LAN computer
using that connection (from computer with LAN IP address) disable default IP address (192.168.88.1) in IP → Addresses (click “D” at the beginning of corresponding row)
reboot hAP lite and verify that everything works
The first bullet is there to avoid complete reconfiguration of hAP lite which by default configures ether1 as WAN connection and all traffic between that port and all the rest is subject to firewall, NAT and what not. If you need that 4th wired port for LAN devices, you can get it, but reconfiguration needed is more complex.
I finally got time to follow your instructions, and I want to thank you from the bottom of my heart! Kind people like you make this world a better place.