I watch my lightning node (lnd) routing some amounts. And with lncli feereport I see some sums, let's say 700 sats for this week. But where are those sats? How can I lookup the accumulated routing fees for one channel (not in lncli listchannels) and when do these fees get payed out to my wallet?
The routing fees are charged with successful forwardings. Let's say you received 11 sats on one channel and forward 10 on another you have earned 1 Satoshi. This satoshi increases the total balance of your node and is technically added to the incoming channel. You could of course account the fee to the outgoing channel as that one defines the fee your node charges.
In that sense there is no separate payout of your routing fees as they always directly are added to your nodes balance.
In c-lightning there is a command
listforwardings with which you can examine every forwarding and earned fees on a per channel level. If lnd does not expose such an api you could look in their database as they have to store every old state but that might be tricky.