I am having trouble distinguishing between these when calling for skill tests. Can someone give me an example, say with Machine Cult or Tech Priest, of what questions the different lores would answer?

'Common Lore' would cover general knowledge of a subject, Scholastic Lore covers detailed information, and Forbidden Lore is, well, forbidden: information available only to authorized personnel... or criminals. So, to use your example of the Machine Cult, Common Lore (Mechanicus) would cover the basics- what is within the jurisdiction of the Adeptus Mechanicus, their basic symbols, ranks, and fields of expertise. Scholastic Lore (Mechanicus) would cover details like their history, rituals, specific titles, famous members, etc. Forbidden Lore (Mechanicus) [is there such a skill?] would cover secret teachings, suppressed history, infamous traitors within their ranks, prohibited experiments with warp energy, and things of that nature.

I don't really like how Lores are sub-divided in DH , but I also think the 'Remberancer' system presented in the DH2 Beta is too broad. I hope DH2 's final version falls somewhere in between.

IIRC, there's only FL: Archaotech (or however you spell that), and as the name suggests, it deals with secrets from the Dark Age of Technology.

Common Lore (Physics): objects in motion continue to remain in motion unless disturbed by an outside force

Scholastic Lore (Physics): Hey I know the formula for that! And it was discovered by an Englishman, Isaac Newton, who was also a theologian, alchemist, and torturer of counterfeiters. He stuttered really badly.

Forbidden Lore (Physics): objects in motion continue to remain in motion unless disturbed by an outside force because of the Devil

Generally you can use the same skill for knowledge with different modifiers.

Knowing that Newtonian Physics is a creation of the Devil might be a -50 Common Lore, -30 Scholastic Lore, or +0 Forbidden Lore Test, for instance. (You might have deduced it by logical inference from textbooks, for instance, even though it's not explicitly stated, but it's a lot harder than if you have actually read the forbidden tome Principia Mathematica et Diabolica containing Newton and the Devil's personal letters.)

On the other hand, knowing that Newton was English might be +0 Common Lore, +30 Scholastic Lore, -10 Forbidden Lore. You get the idea.

Common Lore (Physics): objects in motion continue to remain in motion unless disturbed by an outside force

Scholastic Lore (Physics): Hey I know the formula for that! And it was discovered by an Englishman, Isaac Newton, who was also a theologian, alchemist, and torturer of counterfeiters. He stuttered really badly.

Forbidden Lore (Physics): objects in motion continue to remain in motion unless disturbed by an outside force because of the Devil

This is probably the best description for how it's supposed to work, ever.

'Common Lore' would cover general knowledge of a subject, Scholastic Lore covers detailed information, and Forbidden Lore is, well, forbidden: information available only to authorized personnel... or criminals. So, to use your example of the Machine Cult, Common Lore (Mechanicus) would cover the basics- what is within the jurisdiction of the Adeptus Mechanicus, their basic symbols, ranks, and fields of expertise. Scholastic Lore (Mechanicus) would cover details like their history, rituals, specific titles, famous members, etc. Forbidden Lore (Mechanicus) [is there such a skill?] would cover secret teachings, suppressed history, infamous traitors within their ranks, prohibited experiments with warp energy, and things of that nature.

I don't really like how Lores are sub-divided in DH , but I also think the 'Remberancer' system presented in the DH2 Beta is too broad. I hope DH2 's final version falls somewhere in between.

The only issue I have with how it's done in DH/RT/DW/BC/OW is how it is sometimes left ambiguous due to overlapping naming conventions. This is easily fixed, of course. The whole Remembrancer thing in DH2.. just no. Just because I have knowledge of something doesn't mean that I'm a Remembrancer.

I am having trouble distinguishing between these when calling for skill tests. Can someone give me an example, say with Machine Cult or Tech Priest, of what questions the different lores would answer?

Common Lore is 40K speak for common knowledge. So.. CL: AdMech would be having a general idea about who, what & where the AdMech are - they use a cog symbol, dress in red, come from Mars (and maybe one or two nearby Forge Worlds) they build the manufactoria, they talk to tech through weird rituals, my local Ministorum priest says they're their worship of the God Emperor is improper & borderline heretical.

CL is stuff the Average Joe knows, and you should try to keep all such knowledge in as vague and general terms as you can.

Scholastic Lore is 40K speak for academic knowledge - fields of knowledge you're formally educated in to a fairly high level. Soo.. CL: AdMech would include pretty much everything about the organisation, its history, doctrines, ideologies, major current undertakings/events, and its stand-out individuals. Basically everything that isn't kept secret by the AdMech.

SL is stuff an expert on the Adeptus Mechanicus knows, and you should never ask for a SL test to know stuff you might ask for a CL test to know.

Note: knowledge of the AdMech, whether you're an expert on the organisation or not, doesn't include knowledge of technology. An expert on the AdMech could probably tell you which AdMech world/sub-sect produces a particular plasmagun pattern, but he wouldn't have the faintest idea how plasmaguns work.

It's generally a good idea to test CL and SL directly as rarely as possible. Both skills reflect stuff people "just know", and there's a distinct possibility you're going to make the players feel disenfranchised and their characters moronic, if you test their knowledge skills directly too often. They're generally speaking best used as parts of extended investigation tests.

Forbidden Lore is knowledge that at the very least has the potential to hurt people or organisations. As it relates to the AdMech, it could be something like having a rough idea of how to corrupt a machine spirit, or how to slave together a bunch of cogitators and roughly what to feed them, to produce an Abominable Intelligence.

Forbidden Lore tends to have practical application in some sort of really bad way, and it is often the kind of knowledge you come by, either by doing something very bad, or foiling someone else's attempt at doing something very bad.

Forbidden Lore is a great skill to use as a sort of intellectual awareness test, for example testing whether a PC with the right kinds of knowledge skills, or the right kind of forbidden lore skill recognises odd markings as being of the ruinous powers. You also shouldn't be afraid to punish (mildly!) your players from knowing too much. Having the FL skills to recognise exactly what kind of den of evil the PCs have just wandered into, is a perfect excuse to force a fear test on the overly knowledgeable PC, for example.

I also want to stress that several obstacles or situations can feasibly be resolved by multiple different skills - as it should be - and lores are no different.

So the fact that some lores potentially overlap some is perfectly fine, it just means that you are solving it in different ways.