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.