Recently, while re-architecting a critical module, we encountered a problem wherein we needed to generate PDF from lightning components. Now, being Javascript intensive framework, it has limited room for such features. As of now, there is no native feature within the lightning framework to do so.
Create Visualforce page to retrieve data and generate PDF:
The data exist within Salesforce, it may be a comparatively easier task, by developing a visualforce page, which can accept arguments in querystring and generate PDF by retrieving data via Apex controller.