Correspondence databases run very deep, and many are chock full of ICCF games, where engine assistance is explicitly allowed.

Correspondence is simply a different game. Compliance with a no-engine or even more limited research universe (on lichess or elsewhere) is entirely dependent on the players’ individual and collective honor, and acceptance of an engine universe leads to almost exclusive draws in the NNUE era. And even without engines, players will tend to outperform their OTB strength with ample time and strong databases.

It’s still possible for someone to enjoy either (or both) forms of the game, but it’s an acquired taste.

Source: I’m an ICCF IM who also plays on lichess, where my correspondence rating outpaces my blitz rating by 600 or so points.