Newb question here, do Liches exist in 5th edition? If so, what book are they in?
? afaik, no.
As ExarKun said , not as a specific creature with stats.
You could design one using the rules in either the Faerie or Magic Realm books.
Liches might also be infernal. Many players might think them too fantastic for a typical ArM5 game (in fact, modern liches are a 1977 D&D 
invention with little basis in European mythology).
easy, just get a really, Really, REALLY, REEEEAAAAALLLLLLLLLLLLLYYYYYYYY good longevity ritual
One that does not cause your warp score to increase, I pressume.
Xavi
While liches-as-such don't exist in ArM, the Mystery of the Living Ghost does allow a wizard to become an incorporeal spirit that can possess a human body and whose potency - even if not existence - is intimately tied to his talisman. This is very similar to a lich, and you can make slight alterations to the mystery to make it even more similar. However, as an Hermetic mystery it is limited to creating liches that are 400 years old or so at the most. It is entirely possible that the Hermetic mystery is derived from more ancient pre-Hermetic magic that resembles the D&D liches even more and would allow for liches that are thousands of years old.
The Living Ghost mystery is detailed in The Mysteries: Revised Edition supplement.
External Soul from Hedge Magic ?
As far as I understand them, Living Ghosts need to be bound to specific areas. I see a Lich as something more of a grosser and less effective form of the alchemical immortality mystery, granting immortality at the cost of being an eternal shambling corpse. Something like External Soul fits into the concept too.
I'd like to see a little more in the way of "dark" magic like this within the Hermetic tradition, without automatically bumping over to the Infernal realm. I'd also like to see "Hermetic" magic extend into the past, allowing easier use of ancient secrets by the magi. Bonisagus is supposed to have codified existing magical traditions, not invented the whole thing out of thin air. I can easily see an ancient tradition of necromancers that used Hermetic style magic without having access to the full range of forms and techniques.
As previously noted, no published ArM5 supplement gives rules for Liches. That said, "The Mysteries: Revised Edition" offers a number of different paths to immortality that might serve as models for a homebrew "Hermetic Lichdom" mystery. Lichdom might also make for an interesting Botch result for a magus who experiments with his Longevity Ritual (Original Research is another interesting option)...
I'd recommend some sort of variation on "Living Ghost" with, perhaps, the territorial restriction lifted and replaced with the requirement that the character carry a special staff/pendant talisman created as part of the Mystery (Sacrifice of the character's previous talisman could be part of the initiation).
Or directly "Transformed being" from Real of power Magic, and the Becoming of Merinita fits good. An ancient magical/faeric/sobreenatural being of a Hook/Boon in the Covenant can have clues about that. The Disciples of the Worm or the Donatores (or nearly Cults or Traditions of your game) could offer or need knowledge about that. There are many ways to make it, included directly Epyptian Mommys and therefore.
Thanks to everyone who answered, you've given me much food for thought.
Medieval ghosts in stories were often corporeal. So a D&D style lich actually fits quite well as the ghost of a magus. RoP: Magic would be some help to you but does not actually have stats for such a ghost/creature.
As one who has made it a goal in their current game to create a being "that will never change, has arrested all humors and is at a place of eternal existence between life and death" (my description) I have struggled with making a lich within Ars. I started with the Living Ghost as a template for the mechanics, making some substitutions and saving the body.
Instead of destroying the body (or converting it to magic) I tried to reason that one would make their flesh the place which the Living Ghost is bound, instead of a area of land. There are complications of course with stats, but considering my character is probably 50 years from this goal I got time to work it all out.
I imagined that you would remove your mind and spirit, work the magic to arrest your flesh into a permanent state of stasis so that all the humors and frozen and never changing, and which point you would put your mind and spirit back into the not quite dead body. Then it would be a matter of being bound to that flesh forever, which I guess means you got to take care of it.
Be warned, the character coming up with this is insane and will probably end up dead, but it will be quite a splash!
If I recall correctly, in the first issue of Sub Rosa there was a story that had an old spirit that did that or something similar?
Xavi
In 3rd ed there was a type of Litch described in Wizard's Grimore. This was not a undead creature, but rather a magus that had forgone all but his own magic to live longer. It did not grant a the appearance of a skeleton, but just a slightly paler skin with blue veins (a result of replacing all the blood with a spesial brew).
Converting this to 5th ed, would give us a mystery cult granting transformed being:magic. Ordeals would include no natural healing(can only heal by magical rituals), and blantant gift.
It required total isolation in a non magical area (in 5th ed, I would replace this with isolation in a magical regio), giving up any external magical connections (talisman/familiar), creating a new longevity elixir with among other things dragons blood and something from a pheonix (IIRC), creating a dagger out of extremely purified silver and enchanting it. The dagger would be used to slit your veins when all else was ready, and you would replace your blood with the longevity elixir. There was a considerable chance of just dying during this process...
Ummm... why exactly would it make sense to convert it from a "non-magical" area to a regio which is a place that basically only exists because of magic.
Under the 5th Ed rules , if you have a Might Score , you need to stay in the relevant Aura or it can deteriorate , iirc.
(If thats how i understand your question)
But i though the idea was that they survive by only useing their own magical power (i.e. no items, no familiars, and for the purpose of that rule no auras)
I never looked at 3rd ed It just seemed contrary to what he said before to convert it that way.
durenmar.de/malinbois/library/lichdom.html
Not my work (obviously), Mark Shirley did it.
Gilarius ex Diedne