Third-party APIs that access other users information through OAuth need to be explicitly allowed permission by the user himself.
Normally, this happens through a popup window where the user is asked to allow/reject your app to operate on his data. I'm guessing this is where your issue comes from.
I don't know how linkedin-j does this, but in case you are up for alternatives, you could give Spring Social a try, which has a module addressed specifically for Linkedin. See the Quickstart sample in the page I gave you if you're curious