Best Set Up for Lightroom Classic with a Synology NAS?

It looks like the DS420+ has Gigabit Ethernet ports, so if your computer is connected to it by Ethernet (assuming it and your router/switchers/cables all support Gigabit Ethernet), each 23MB raw file might load in roughly 1/6 of a second (not including rendering if a current preview is not ready), if I am doing the math properly.

If your computer connects to the NAS wirelessly, expect the load time to be much slower, maybe about 1/2 second per image.

Gigabit Ethernet is much slower than USB 3, so if you had an NAS or DAS that you can also connect directly using 5Gb/sec USB 3, each file might load in about 1/10 to 1/20th of a second. Some NAS/DAS have 10Gb/sec USB 3/4 ports, to cut load time further, if the files are stored on a fast SSD. Another way to speed the transfer time is to use an NAS with a 10Gb/sec Ethernet port to match USB 3, but that gets expensive because again, everything about the network would have to support 10Gb/sec Ethernet including your computer.

Questions about NAS only cover the transfer time to get each frame from the NAS to the computer. Other performance aspects are controlled by other things not related to the NAS: 

• If you are interested in faster frame-to-frame display time in Loupe/Grid, that has to do with having at least 12GB RAM available to Lightroom Classic, so that it has enough memory to build a RAM cache of previews. 
• If you are interested in responsiveness while editing or how quickly previews are generated, that has to do with the speed and number of your CPU cores plus (up to a point) the specs of your GPU. 
• If you are interested in how quickly edited raw images load into the Develop module, make sure the Camera Raw cache is on an SSD, and to some extent it helps to increase its size. You control both in Lightroom Classic preferences, in the Performance tab. 

Note that by default, your edits to raw files are not sent back to the NAS. They are stored in the Lightroom Classic catalog, which is presumably on your computer (and cannot be stored on a server). The actual previews file is in the same folder, also on your computer and not the NAS. The only times edits are sent out to the NAS is if you enable saving an XMP sidecar file for each image, or when editing or exporting non-raw files to be stored on the NAS.

I have the opposite opinion. Unless there is some malfunction, photos on the NAS are fine, you won't really notice a speed in difference in Lightroom Classic regardless of where the photos are stored. (But you still need backups of your photos and catalog file)

IMO, use the NAS for backups, use a hard drive, be it internal or external, for primary storage of photos.