What type of airspace is an Atlantic Low Control Area?
The Atlantic Low Control Area is a Class E area in international airspace, where domestic ATC procedures may be used for separation procedures.

Here are the relevant excerpts from FAA Chapter 19. Other Airspace Areas
Section 1. General


  Offshore/Control Airspace Areas are locations designated in international airspace (between the U.S. 12-mile territorial limit and the CTA/FIR boundary, and within areas of domestic radio navigational signal or ATC radar coverage) wherein domestic ATC procedures may be used for separation purposes. 


and


  Class A Offshore/Control Airspace Areas are identified as “High" (e.g., Atlantic High; Control 1154H). Class E areas are identified as “Low" (e.g., Gulf of Mexico Low, Control 1141L)


The two parallel lines differentiate floors of class E airspace that is neither 700 feet nor 1200 feet AGL (Above Ground Level).