use of engines in correspondence games

I don't think it is allowed cuz then everyone would use it and then no-one would improve

#11
In ICCF everybody uses engines as allowed. If you just follow an engine on ICCF, then you get beaten.
ICCF is about analysis beyond the horizons of the engines.

#12 This matches what I read in the old days in an article in Chess Life by a top player. The author of the article laughed at the idea that you could do well in correspondence by playing what some engine thought was "best". He meant at the top level, of course.

Maybe dont call it correspondence chess to avoid confusion with ICCF rules?
On chess.com they call this mode Daily Chess, with same rules as lichess (no engines, opening books allowed).

Honestly it does make some sense for GM's to use computer's assistance, to discover interesting ideas and so on.

I have a question thought. I'm playing a correspondance game, and my opening book advice a move A. I read the book a bit, and it says that of the two natural answers B and C, only B is playable without more explanation. I play around with the engine to understand why C isn't playable, and after I understood it, I play the move A. Then my opponent play the move C. Then play continues, without the help of the book (as it doesn't say anything about C), nor the help of engines, only what is remembered of the previous analysis.

Is that legal (on lichess obviously) ?

In principle lichess prohibits engine use during the game, so what you do would be illegal on lichess. However lichess has no way to detect that.
Lichess cannot know if you consulted the engine before the game (allowed) or during the game (prohibited).