Can I use Lucky Cigarette Case to increase a fail roll 1 on 2 and thus avoid activating dark pact condition?
(2) Lucky Cigarette Case
Trinket
Once per round, you may add 1 to the result of 1 die when resolving a test.
No.
Its effect only applies to tests (where you test one of your Investigator's five skills).
It does not apply to checks like the Dark Pact condition has (or any other check where you roll a dice without reference to a specific skill).