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Please share additional information regarding your setup:
1. Ethtool -i output of your Intel Ethernet controller
2. LLDP utility used
3. Brand and model of other NIC without the issue
4. Linux distribution and kernel version
I've done some more research on my scenario, and there was another mid device that actually filtered those LLDP packets.
Sorry, my bad. There is nothing wrong with i354 when it comes to LLDP.