This really should not be too hard to implement since Visio can accept data from a host of different sources including MSSQL databases, which if I am not mistaken is how Lansweeper stores it's data. Even if it is not a MSSQL database, it is probably ODBC compatible.
In the short term what I have done to get this functionality (import Lansweeper data into Visio diagram) is to export a custom report with the data I want as an Excel sheet, then connect to that Excel sheet. You do need to manually connect the data to the shapes the first time, after that however simply updating the spreadsheet (by doing a new export to the same file name) is enough to update the Visio drawing.