With Social Member Lock you can not only let your users connect with their Facebook or Google Plus account, but you also have the ability to let them connect with their LinkIn account. To be able to add that to your Social Membership, you need to create an Application at LinkedIn and enter its details in to the specific settings as shown in the image below:

 SML LinkedIn

*This step is required in order to use LinkedIN Connect for your Social Membership. 

Go to the Creating A LinkedIn App Knowledge Base page to see a complete step by step tutorial on how to create an Application for LinkedIn.