Lokalise API v2 operations are performed using HTTPS GET or POST requests passing data as request query parameters for GET and URL form-encoded for POST. To send an API request, you'll require an API token (please find detailed information in the following doc).
Responses are encoded as JSON objects. If the operation was unsuccessful, the JSON object will contain an error code and a message. There is Lokalise CLI tool acting as a wrapper for import and export functions. You can download a precompiled binary for different platforms.
Full API reference and the list of official API clients is available here.