In its essence, Lightning is basically a client-side, browser based framework. It mainly deals with how the data is displayed on the page or how a user interface is presented to enable inputting of data.
Accessing offline data, or even on cloud data is part of a backend and thus you can surely achieve it using the lighting component. However you would need a native container for web or mobile (for Android or iOS app) that would aid the component in the task.
EDIT: I am assuming you are creating a Lightning component based visual force page or web app.
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This reply was modified 9 years, 12 months ago by
SFDCHacker.