If enabled in the tenant, you can share SharePoint objects to external users. They will be required to set up a Microsoft Account before logging in. There are some caveats though:
- User must click the link within a time frame
- User can use any email they like once they have the link. They do not have to use the email it was sent to.
To enable sharing on the tenant level:
- From the SharePoint admin center, click sharing.
- Select an option that starts with Allow... (or select **Don't allow...* to disable sharing).
- Click OK to save the settings.
See this link for more information (including directions on how to enable per site collection instead of tenant-wide).
This link has directions for sharing sites and documents to external users. The directions for sharing sites mostly apply to libraries and list as well.