Complex sentence: There is a connection to the Lower Montauk Branch, but, no LIRR trains run on that branch, and the Lower Montauk is now leased to and controlled by the New York and Atlantic Railway, which uses the line exclusively for freight operations.
Split into simpler sentences: There is a connection to the Lower Montauk Branch; however, as of, no LIRR trains operate over that branch. The Lower Montauk is now leased to and controlled by the New York & Atlantic Railway, which uses the line exclusively for freight operations.