1) At the end of Nikola's Cooperation - Consideration or Art of Persuasion, whatever you have chosen after Relic Exploration, you got "Loraine's Certificate". If you want to do this quest and its sequel, Vain Conclusion, you must destroy this quest item by dragging it with your mouse cursor to the trash can in the lower right corner of your Inventory screen.
2) Then, when you are level 41, talk to Researcher Lorain again.
4) Nikola is still at his old position, somewhat southwest of Lorain.
7) Dorothy accepts the challenge and gives you 98,583 adena for your trouble. If you are between level 41 and 46 you will also get 285,935 exp and 18,711 SP.
When you are level 42 you can come back to Dorothy and pick up from her the final quest in this series - Vain Conclusion.