On the spot I would ask for a rewind.

Putting more thought into it, the player originally knew what the top 2 cards of his library were, the disruption to the game would come from not knowing this information after the rewind. This would be the case whether he drew 2 cards, 7 cards, or 11 cards. There are differences between those cases but I would want my decision to remain consistent for each of them. I can also see reasons why there would be a difference in the decision between 2 cards or less drawn and 3 cards or more drawn.

I think I would rewind here. Changing the order of 7 cards in the top of a library, even when the top 2 are deliberately there, doesn't seem such a big disruption to the game to justify leaving Lili on the stack.

So we need to look if we meet the 2 conditions to do a rewind according to the IPG. It's definitely a reasonable time to decide to rewind (only 1 ability away from the mistake), and I think the complexity of the situation is not that high (but I understand that for some judges this second condition could be complicated to accept). So, for me, both condition met, rewind asked.

Drawing 7 is a big disruption. That is a lot of knowledge, and 7 random can really change the game. I am loath to back up through that. So I have to side with no backup. The interesting partvto me then is I assume Lilliana is still on the stack, so if we leave it there the Griselbrand player can still respond with whatever they were going to.

I'm in the no rewind camp myself.

The biggest decision since the illegal action is a player choosing he wants the two cards he knows a five random cards, choosing to draw two or three is normally a big choice that needs serious consideration to back up but seven in total is huge. That player will know the top seven cards, not the order granted but what is possibly there, this could then potentially effect the next seven turns (if he choose never to use Griselbrand) of the game due to that knowledge, however letting Liliana resolve will only have a known potential effect of this turn.

No backup for me.

As a HJ, I rewind as part of a GPE-GRV fix when I'm able to get a clean game state as a result. This is a good service to the players as it allows them to continue the game they were supposed to play, despite the fact that they both failed they responsibilities.

I don't rewind if that means that I would replace a messy game state with another messy game state, trading one mess for a different one. That not only doesn't really fit the whole “continue the game you were supposed to play” situation, but also open too much the door to perception of unfairness and bias.

I'd also note that the IPG ask that the backup “is simple enough to safely back up without too much disruption to the course of the game”, not “less disruptive than leaving the game state as it”. I interpret this as needing to judge the backup's disruption in a vacuum, and not compared to the current disruption caused by the GRV. Shuffling brainstormed cards up to 7 cards deep is “too much disruption” for me.

While I would probably ask for a backup if I was given the call, not backing up seems better supported by the IPG.
But I would still find it very hard to sell to the player the we will do nothing because “he is also responsible for maintaining the gamestate”. I would think almost all players, given this situation, would appeal to the headjudge and consequently would feel cheated once the HJ also decides not to back up.
Any tips as to go about explaining that he will now likely lose to a planeswalker that could not have been cast legally, just because he used an ability to try and stop it from resolving?

While the document states to not backup when this would cause “to much” disruption, I would guess that a lot of judges do weigh both backing up and doing nothing, and go with the “lesser disruptive” option.

We had a somewhat similar situation at our January judge meeting.

I feel that I'd rule the same way here as I did there - Backing up is a great disruption, so I will not back up - but at the same time, I see the argument pro Backup, since the ‘net-disruption’ when backing up can be seen as lower than not backing up. Though even that is a close call to me, as ‘illegaly casting a spell’ might not outweigh ‘knowing the top 7 cards of the library, though not the order’ plus ‘not knowing the top 2 cards of the library even though I should’.
Note that I did not include the 7 cards drawn in this comparison of disruptions, as drawing the seven was not illegal, and can still be done again if we rewind - though the player might choose not to do so as he now knows that he draws 7 lands, and shuffle beforehand.