Lead supervisory authority (LSA)
The lead supervisaory authority (LSA) will be the authority of the principal place of business, i.e. the place of the head office in the EU.
If you do not have a central administration in the EU, then it will be the establishment in the EU where the essential part of your processing activities takes place. For example, a commercial office.
The so-called "one-stop shop" mechanism allows organizations that carry out cross-border processing (establishments in more than one EU member state or processing operations affecting individuals in more than one EU member state) to interact with a single national supervisory authority that will make decisions applicable to all member states affected by the processing.