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Lan-play and LDN do not work together.
The Ryujinx LDN build makes using the Local Play/Local Wireless connection usable in games that have it by simulating you and other LDN build users as being "in range" of each other's emulated Switch wireless radios.
The
Lan-play.com application works by creating a VPN tunnel for your hacked switch to convert LDN games into LAN traffic that passes over the VPN tunnel to others using Lan-play. This requires a 3rd party custom module call ldn_mitm in order to work.
To connect Ryujinx to a real switch, the game first needs to support LAN mode natively. Then the two sides (Ryujinx, and the Switch) need to be on the same network. Ideally locally, but at least a couple of users have had success with VPN.