Unfortunately, Lansweeper currently only offers and API for the helpdesk module to create, retrieve or update tickets. An asset API has been requested before and is already on our customer wishlist. We've moved your topic to the wishlist section of our forum in this context. For now we don't have an estimated release date yet for an asset API.
The way we'd recommend retrieving information from your Lansweeper database currently would be via SQL queries. You could create a view that contains all the information you're looking for and export/import it. If you want to interface with your Lansweeper database externally, the connectionstring of your Lansweeper database can be found in Program Files (x86)\Lansweeper\Service\lansweeperservice.exe.config on your Lansweeper server or by opening ConfigEditor.exe under Program Files (x86)\Lansweeper\Tools if you're on version 6.0.100.