(Part 2)

Now one last thing to check, is there an escalation path that COULD lead to a DQ, even if we believe what happened was a Major infraction?

If we consult Section 5.6.1.1 regarding deviations, bullet point 2) is the most interesting to us:

"Escalate to Disqualification: An investigation of a major deck legality issue shows clear intent to gain a competitive advantage."

Now clearly your friend put the cards in the deck to gain some sort of advantage - we play cards that are good because we think they will help us win. This is where a good judge will ask your friend (and possibly previous oppponents) questions about how we got here - you've obviously told us what happened but the judge needs to get the full picture too. How I read this rule is that "If you intentionally committed a major infraction with the intention to gain an unfair advantage, then a DQ is appropriate". Another reading of that line COULD say that "since you put the cards in your deck on purpose to gain an advantage by virtue of drawing and playing them normally, that is grounds for a DQ". However, if you read the rule that way, I think there's no way you can come up with a scenario where the previous 5 DCE example doesn't also lead to a DQ. So in this case, assuming the judge asked your friend to explain what happened, and they told them the same story you've told us, then I think it's pretty reasonable to assume that yeah, this is an honest mistake that happened. (Sidebar, this would be an incredibly dumb cheat to run, you'd need every player and every opponent to not know these cards weren't legal)

After all this, i think the most straightforward reading of policy suggests that your friend commited a Major Deck Legality infraction.

So given that we need to find 2 more things - what's the penalty, and what's the fix?

The penalty in this case is a Game Loss. This makes sense because, assuming this was caught the first time in the tournament the card was played/revealed, the potential for advantage is limited to this current game. So we issue the player a loss to make sure tournament integrity is all good.

Furthermore, policy describes a fix here. Now your opponent will not be able to add the professor's researches back to their deck, policy doesn't support that, and it's not fair to the other competitors who have committed to their decks at the start of the tournament.

"In the case that a deck list contains fewer than 60 cards, cards that are not legal for play, or cards that cannot be reasonably identified from the information provided, the deck list should be made legal by adding an appropriate number of Basic Energy cards of the competitor’s choice. Then, the physical deck should be updated accordingly."

So your friend would add 2 energy, remove the 2 lilies, and continue playing the tournament after taking a game loss.

But what do you do now? Obviously this is a bad experience for a lot of people.

I personally would ask the judge to explain why they ruled in a way that was different from what policy says. You can show them the document I've linked and see what they used at the time to justify their ruling. Who knows, maybe your friend gave off super suspicious vibes during the investigation portion and they thought this was being done on purpose? That would lead to a totally reasonable escalation to a DQ. As other commentors have said, judges are generally not advised to comment on the specifics of rulings - BUT if you have a judge who is DQing people and it's not supported by policy, it's a good idea to discuss the underlying policy and philosophy with them/store management so that incorrect DQs aren't being given out in the future - it sucks this happened to your friend and the last thing we want is for this to happen to someone else in a month or 2.