Given the requirements you gave above together with your answer to my question I believe you won't need a workflow to link all three items together. I have two options for you:
1st Option:
- Create a General Responsibility list. This list should contain at least two columns. The ID and Title column.
- Create an EMS Responsibilities list. This list should contain at least three columns. The ID, the Title column and a lookup column linked to the General Responsibility list.
- Create a Document Library. Add a lookup column linked to EMS Responsibilities.
Since the lookup list you are using is already linked to General Responsibilities then there is no need to have another column solely dedicated to point to General Responsibilities. If however, you need to have specific columns in your document library so that it explicitly has columns for both General Responsibilities and EMS Responsibilities use option 2 below.
Option 2
Create a General Responsibility list. This list should at least contain the ID and Title column.
Create an EMS Responsibility list. This list should at least contain the ID, lookup column linked to General Responsibility and Title columns.
Create a document library. You should add two lookup columns. One pointing to General Responsibility the other to EMS Responsibility.
(now the fun part starts)
Follow the guide to edit both your NewForm and EditForm aspx in this link so that your lookup dropdowns will be a cascading dropdown. This will make sure that items from EMS dropdown will only be populated once you select a value from the General dropdown.
Let me know if you need any more clarifications.