Lokalise supports InDesign files in IDML format. These documents do not require any special formatting, but please note that they can only be uploaded to projects with the ad hoc documents type. The project type is selected upon creation:

For example, let's proceed to the Upload page and import a small IDML file. After the uploading is completed, you'll see all texts being extracted from your file:

To download your data in IDML format back, choose the corresponding option from the Format dropdown on the Download page: