So, diaglo, does it ultimately come down to a Dex roll, but the decision as to whether the roll is allowed at all depend on the factors you describe above?
Anyway, as per your request...
Penelope Paladin is a 5th-level Fighting Man with Dex 15. Her AL is Lawful (they didn't do Good or Evil yet in OD&D, right?). She is a dedicated knight and a very moral person. Assume she is presented with the opportunity (lighting, situation) to pick the pocket of a vile moneychanger who has refused to give back a pouch of money he collected from an orphanage on dubious terms. She goes for it, feeling the good of getting the money back to the orphans outweights the petty crime of theft from a person she considers "evil".
Randy Rogue is a 5th-level Fighting Man with Dex 15. His AL is Neutral. He's been a street urchin most his life and has had to survive by his wits. Sometimes he'll take honest work, sometimes he'll be happy to steal. He sees the local moneychanger has just collected a hefty pouch of coins. Opportunity (lighting, situation) presents itself, and Randy tries to pick the moneychanger's pocket.
The moneychanger is a John Doe, 0-level whatever.
Which PC has the better chance? Does Randy have the edge because he's streetwise, or does Penelope because she feels right is on her side? Do both boil down to 3d6 vs. Dex? Are modifiers involved?
Inquiring minds want to know!