Only if you toggle local-evaluation in the analysis board. When you "request a computer analysis", the computation is done by fishnet [1] on volunteers' hardware.
But can you request a computer analysis with fishnet anymore? I have a non-patron account and I can't find that option anywhere. Old forum posts seem to talk about it working by pressing Z and being limited, but when I press Z I get a message that it is disabled by default and a link to enable it. When pressing to enable, nothing happens.
It's been a while since I used Lichess anonymously, but I suspect you do need an account to request a server analysis – that way they can limit the number of analyses per day for a user [1].
You don't need to be a patron, you just need an account. One of the many amazing things about lichess is it's 100% free and donators get no extra privileges except a little logo next to their user
Except fishnet is used to analyze broadcasted games, puzzle discovery and others. Not used when analyzing your own games. You can easily test this by opening your task manager, monitoring your CPU usage, then opening a game you played on Lichess and toggling the aptly named "local evaluation". It's the toggle bar on the upper right, next to the text "Stockfish 14+ NNUE in local browser". You will see your CPU usage increase while the evaluation is on.
No, that is an analysis of a single position, not a game. The big button under every game which says "Request Computer Analysis" is done on fishnet as well, it literally says "Stockfish 14.1 server analysis".
That is true when you’re playing in your browser.
On the mobile app (at least the iOS version) you can request computer analysis for your game done on the server.
[1] https://github.com/niklasf/fishnet