@user2185482, from the documentation Prabhat provided, you can see that inline editing like you want is only possible if all records are of the same Record Type.
As you said, you'd like to filter lead list views based on the company, not on the record type. However, if such a filter shows leads with different record types, you won't be able to do inline editing, and will have to edit from within each lead.
The solution (assuming no custom coding) might be to have all your leads stay as a single record type until your organization's Research Team goes through and assigns them to your users. Then have workflow rules that update the newly assigned leads' record type as appropriate.
- All leads prior to review by Research Team are set to one record type, maybe call it 'Pre-Assignment', or 'Waiting on Research Team'. You get the idea.
- Create a workflow rule for each Record Type you plan on updating leads to after being assigned.
- Logic for each workflow rule could be something like "If lead has been modified by Research Team and has been assigned to a user, AND lead meets the criteria demonstrating that it belongs to Record Type Y, then update to Record type Y"