I might be a bit late on this, as she is now seeing some gameplay, even more just before rotation, when Mutilate was still legal. Still, I don’t think Liliana of the Dark Realms gets the recognition she deserves.
Like most Planeswalkers, this one might just eat a counter or Hero’s Downfall, or worse yet, just save you from some damage. However, what do you generally want from you planeswalkers? Two things: recurring card advantage, and an ability to protect itself. Liliana can do both of these things.
First, she can get you a swamp each turn. You won’t be able to use them all, if you use this ability each turn, but you are still thinning your deck, letting you draw more gas. Never missing a land drop is great, if you don’t have to get flooded to do it. Liliana is very good in this regard.
Second, her second ability has much synergy with the first one. Her main problem is that she can’t use this ability the turn she comes to play without getting rid of herself, but if she could, this card would be ridiculously good. If you are playing monoblack, this is still a good option. Lets compare: Lash of the Whip is an instant with casting cost of 4B, which give target creature -4/-4, same as our Liliana on the fourth turn, if playing monoblack. Granted, that the Lash isn’t exactly constructed playable, but we still see that Liliana can do something the R&D (mostly the D) sees are very valuable in terms of mana. And this is if Liliana is played on the fourth turn.
If you play her later, destroying the indestructible Gods is a matter of routine for our heroine. If you manage to keep her alive, this may happen plenty of times. This was easier before the rotation with Mutilate, but its still doable with all the spot removal available. So basically, this is another form of recurring card advantage.
… and this ability has another side as well. I’ve oneshotted an opponent in standard with this ability. I was very flooded, but managed to use Liliana to kill enough opponents creatures to keep him from killing me. The game went pretty long (well, 15 rounds to be exact). Then I pumped a Vampire Nighthawk into a 17/18 and killed him by attacking exactly once.
Then there’s the ultimate ability. Well, since I don’t build my decks around it, I actually have never had any real use for it. The one time I managed to ultimate her in standard, I did have a Griselbrand in play, but I had gone through most of my deck by that point and couldn’t really draw any more cards. The one time I ultimated her in EDH, I did it just to be able to use the emblem at least once. Again, I didn’t really have a use for it. I think I did sacrifice a Gravecrawler to my Grimgrin, Corpse-Born for a couple of dozen times, but that was unnecessary and somewhat risky, as there was always the risk of some stealing my GG.
Still, its nice to have four times the mana.
Also, I should note Liliana is my favorite of all the planeswalkers just as a character. Not that I’ve read the novels (except for one early, maybe the first MtG novel back in mid-90s), but she evokes the most interesting character just through the cards (and maybe the comics on the Wizards website, although they try to make her look more relatable by making her past more tragic).