Did you receive the micro tip a couple of days ago? 1 satoshi and 1/500th of a sat as the TX fee.
1 satoshi arrived at tippin.me 
I didn't check it earlier as nobody (else) uses it 
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I now have 1.0002 sats more I can receive from others, so it looks like no lightning node receives any of the TX fees so the Lightning Network could possibly be a closed system?
The Lightning Network is a closed system indeed. It seems your node charges 0.2% fee on all transactions, including small ones. For bigger transactions, other nodes in the channel might charge a fee too, so the node you're connected to pays them part of the fee.