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A roll of 1 is normally an automatic miss regardless of modifiers. A roll of 20 is a critical hit.

Do Lore dice affect this?
I'm tempted to rule that they do, because the right knowledge could effect these outcomes in some cases.
In that case you might use the Lore die to augment your roll of 1, in which case your other modifiers might allow you to hit.
How about criticals, can you use a lore dice to boost your roll to 20?
In addition, my interpretation is that since the lore die is added to the roll, it is not a modifier but instead it creates a bigger die roll.

It's an interesting thought.

Just one comment, it occurs to me that if you do this, a hero using a keen or superior keen weapon (gets a critical hit on a 19 or 20) would be getting attack crits way more often than intended. Looking at a dice probability website, crit chance jumps from 10% (a natural 19 or natural 20) to 27.5% (d6+d20>=19). That's a pretty huge increase. A hero with such a weapon would be double rolling damage dice way more often.

That's certainly a possibility. I ran a game yesterday where the players battled some trolls. I have a 3rd level scholar NPC who can grant them some lore dice so they were able to use them during the battle. In this case they used them to score some hits on attacks that would have missed otherwise and none of them got higher than a 3 on the lore die. They did get some crits but all on natural 20s so it didn't come into play.
I'm going to keep play testing it that way with my group but I am still very interested in finding out how it is actually supposed to work within the rules.

In the D20 system, the Critical hit/automatic success on a "20" or an automatic miss/fail on a "1" is meant for the d20 only, not any other bonus dice. This rule only applies to attacks and saving throws, not ability checks. If you include the bonus dice, you can never have a "1" and the possibility of a "20" is greatly increased, even more so if you call it 20 plus.

For example, in core D&D, the Bless spell lets you add a d4 to your attack or save. If you include it as part of the d20, the range is 2-24, not 1-20. That's no "1" and five results that might cause a critical hit. It also puts a bell curve on the results (which occurs every time you add dice) with an average of 13.

Bonus dice are supposed to be added to the result, not the roll; the same as modifiers.

Thanks jlandon, I appreciate your input on that!