@Rafael, we have already followed the same procedure as you have said. Let me explain my concern below.
After executing the Lifecycle mapping, we are able to get all the properties value for Processor in Deployed Asset application. Then, after executing the Inventory mapping, value of the properties which are similar in both Lifecycle and Inventory datasource displayed under Processor in Deployed Asset and rest became empty.
Next time when we execute the Lifecycle mapping, all the properties value are coming back. Again if we execute the inventory mapping, dissimilar properties become empty. This is happening because the properties which are available in Lifecycle datasource are not same as Inventory datasource and everytime they execute they replace the properties value as per their datasource properties.