I have heard from a friend of mine that Islam directs all the Muslims living in non-Muslim lands to unite under one leadership and present  themselves as a single entity. Is this true?

I am afraid that nowhere has Islam directed Muslims living in a non-Muslim country to unite under one leadership. This may serve their interest and be very beneficial for them. However, they have not been bound by their religion in this regard. It is up to them if they want to adopt such a policy.