Okay, now that you're starting to behave, I'll give you the benefit of my wisdom

.
To be honest, while this spell may not be "broken", it *is* Uber. And those that are shrugging it off are, IMHO, giving your argument short shrift, probably because you were such a bastard at the beginning. But let's move past that. . .
Nothing about the spell suggests that it can't be used on someone on another plane, or in an extra-dimensional space. The Range is "Unlimited", and there are no comments about it not affecting those on other planes, like there are for other spells with essentially unlimited range, like
Teleport and
Scry. The
Rope Trick idea doesn't work.
Because the rules do not say that this is a divination/location spell,
Non-detection doesn't work. (I would rule that an implicit part of
Nightmare is the ability to locate the creature who is dreaming, and so would probably allow
Non-detection to possibly foil the spell, but that's a Rule 0.)
In fact, as best I can tell the only spells that allow one to stop the effect are an
AM Field and
Mind Blank.
So, suppose this lich *does* have either minions, or a fantastic Will DC. The "hey, you'll eventually make your save" crowd gets a thumbs down -- if there's multiple castings, you're probably screwed 90%+ of the time. Sure, at least one minion will be spending most of his time in a trance to get you (which means they really, REALLY must hate your guts -- why did you piss off such a powerful lich, Brilliantus?), but if they want to do it, that's their right.
So let's look at your options:
1) Ring of Sustenance, followed by 6-8 hours rest. At least one minion will have to Trance to nail you at the right time. If he fails, he'll go tell his lich boss and his buddies to start casting. With the multiple castings involved, even if one guy gets Dispel Evil'd, some other guy's Nightmare will probably get through to you. A group of 4+ staggered Dispel Evils *might* protect you, given the spell's long casting time, though. It's a crapshoot, but it's one that you'll probably win 50% of the time. Assuming you've got a cleric that can cast 4+ Dispel Evils a day. (Which, to be honest, you probably do, if he can memorize them in his 6th level slot.)
2) Ring of Sustenance/8 hours rest/AM Field. Doesn't work because the Ring won't work in the AM Field. Never mind.
3) Mind Blank. If you're pissing of a lich and his 9th level+ minions, then you hopefully are high enough level to have someone cast this damn spell. But it's not guaranteed, especially in a challenging campaign.
4) Whine on the EN Boards. Done, and done. But it's not helping so far, is it?
5) Come up with a new spell that protects one's sleep from nasty dreamy intruders. Heck, call it "Deep Sleep". 3rd or 4th level abjuration spell.
BUT let's say that
1) Your DM won't Rule 0 Non-detection or Prot. Evil so they're protective against this,
2) He won't Rule 0 that Nightmare doesn't work across planes,
3) The lich has multiple 9th level minions that know how to work as a team (and they all REALLY hate your guts),
4) You can't come up with a "Deep Sleep" spell at this juncture in time, and
5) Nobody has Mind Blank.
6) You don't have BOTH a Ring of Sustenance AND a cleric that can cast multiple multiple Dispel Evils.
Unlike everyone else in here, I feel your pain -- this is not a completely unlikely set of circumstances, and it's a set that reams you good. It's probably time to either
A) Retreat and return when you have a defense against the spell, or
B) Let your party buddies do the work, because you're admittedly pretty damn defenseless.
I vote for "A". Sometimes the bad guys are more powerful than the good guys, and there's nothing you can do except leave, regroup, and come back better prepared.
Suck it up, man! The DM min-maxed some baddies. You should be glad to have a DM that doesn't have his NPCs roll over for you.