Lich ascendancy "Eternal Life" disables hp regeneration from any source until player gets damaged.

City Wells should restore HP even with the "Eternal Life" active, since when changing equipment, the value of the current HP takes on the same value as if the item is missing and can only be restored by deactivating the "Eternal Life" node. And this is not free at all.

Yes I can totally reproduce this problem for Lich with eternal life. The fountain and the potions should recharge this.

I agree, there should be way to recover life out of combat. The well could work as a temporary solution, but it would force you to recover life (even if you don't want to) when you just want to refill flasks, which is not ideal.

While I haven't tried the Lich yet, it's not hard to imagine how you lose some life with each fight making your effective HP lower and lower. And when you're at 10/1500 life, you know you're going to die the next time, and there's nothing* you can do about it. Now when bleeding is applied through ES, the issue should escalate.

I don't know, maybe this limitation is justified by flavour, like: life fades over time but after death the lich rebirthes full of strength (phoenix theme) or eternal life comes at the cost of weakening in battle. But I doubt that's what the designers thought about.

*Nothing without getting out of character, you have to get rid of ES, or wear the EB helmet, or respec Eternal Life, etc to recover life. So it's still ultimately possible, and players do that constantly, but they must resort to such annoying (and lame, to be honest) get-arounds. I want to believe it just wasn't clear at the design stage for the devs that this notable would bring lots of incovinience, so they didn't add a way to recover life out of combat preemptively.