I like the MTG rules for this situation. In short-hand:
- "Skip a turn" effects are replacement effects (because "skip a turn" effectively means "instead of taking a turn, don't take a turn").
- When multiple replacement could be applied at the same time, you choose one to apply (same rule as Dominion, really).
- You repeat this process of picking another one
if there are any left to pick.
- "If an event is replaced, it never happens". (Direct rules quote).
And
Anything scheduled for a skipped step, phase, or turn won’t happen. Anything scheduled for the “next” occurrence of something waits for the first occurrence that isn’t skipped. If two effects each cause a player to skip their next occurrence, that player must skip the next two; one effect will be satisfied in skipping the first occurrence, while the other will remain until another occurrence can be skipped.
What this means is that when you have 2 "skip your next turn" effects out there, and you are about to start a turn...
1. There are 2 replacement effects that could apply, so you choose one of them. You replace "start your turn" with "do nothing". (You choose Lich #1).
2. You check for other replacement effects to apply. There are none, because there is no turn about to start anymore, that event has already been replaced.
3. Lich #2 is still sitting around waiting for a turn to begin so it can skip that turn; because Lich #1 was applied to the last would-be turn, Lich #2 never had a turn to skip.
I think this matches up well with how other "replacement effects" in Dominion work. There are very few of those... but 1st edition Trader is probably the simplest example:
You are about to gain a Curse. You have 2 Traders in hand, so 2 different potential replacement effects that could replace this event (granted they are only potential replacement effects, because you would have to choose to reveal them, which is slightly different than replacement effects which are already there, like Lich). You reveal Trader #1. Now that Curse gain has been replaced; it never happened. You cannot reveal Trader #2 (or Trader #1 again) to replace that Curse gain; there is no Curse gain. (Of course you can reveal Trader 1 or 2 to replace that new Silver gain, but that's completely separate).