I don't think there is a native way to do it.  But I have a process that does this via a custom view I added to my LFForms database, and a workflow to generate and send the emails on the weekly schedule.

I posted the database view on another post yesterday, so I'm just linking to that here.

The Workflow looks like this:

1. We start with a Custom Query activity to get the list of users that have items that are past due.  This query specifically gets items 7+ days past due.

   SELECT [Assigned to (username)]
         ,[Assigned to (email)]
   FROM [LFForms].[dbo].[active_processes_view]
   WHERE [Step due date] <= DATEADD(DAY, -7, GETDATE())
   GROUP BY [Assigned to (username)], [Assigned to (email)]  
   

2. Then we use a For Each Row activity to loop through each user returned on step #1.
3. Within the For Each Row activity:
   1. Create a multi-value token named "Form Details".
   2. Run another Custom Query to get the list of forms that are assigned to the specific user.  The custom query passes in two tokens as part of the query (the two ? items assuming you are using ODBC connection).  Those are: %(CycleThroughEachUser_Assigned to (username)) and %(CycleThroughEachUser_Assigned to (email))
      Once again, this is searching 7+ days past due.

      SELECT [Process Name]
            ,[Instance name]
            ,[Started by]
            ,[Last updated]
            ,[Assigned to]
            ,[Assigned to (username)]
            ,[Assigned to (email)]
            ,[Current step]
            ,[Step start date]
            ,[Start date]
            ,[Instance ID]
            ,[Step due date]
      FROM [LFFormsTest].[dbo].[active_processes_view]
      WHERE [Step due date] <= DATEADD(DAY, -7, GETDATE())
        AND [Assigned to (username)] = ? 
        AND [Assigned to (email)] = ? 
      ORDER BY [Start date] 
      

   3. Then we use a For Each Row activity to loop through each user returned on step #3.2

   4. Within the For Each Row activity
      1. A Conditional Decision activity that is based on whether the iteration of the current row is either divisible by 2 or not.  This just determines and even/odd pattern. 
      2. In either even or odd, we're going to append to the Form Details token, the only difference will be the start of it that sets the background color.  This is going to create an HTML structured table row, with the contents of the current result.
      3. The added value will look like this - again, the only difference is the color at the beginning - this example is white, and I use that on the odd rows, and for the even rows I use a darker color - this makes banded rows in the table.

         <tr style="background-color:white;"><td>%(CycleThroughEachFormBelongingtoUser_Process Name)</td><td>%(CycleThroughEachFormBelongingtoUser_Instance name)</td><td>%(CycleThroughEachFormBelongingtoUser_Started by)</td><td>%(CycleThroughEachFormBelongingtoUser_Last updated#"MM//dd//yyyy"#)</td><td>%(CycleThroughEachFormBelongingtoUser_Assigned to)</td><td>%(CycleThroughEachFormBelongingtoUser_Current step)</td><td>%(CycleThroughEachFormBelongingtoUser_Step start date#"MM//dd//yyyy"#)</td><td>%(CycleThroughEachFormBelongingtoUser_Step due date#"MM//dd//yyyy"#)</td><td>%(CycleThroughEachFormBelongingtoUser_Instance ID)</td></tr>
         

   5. Now we'll email the user (using the .  

      1. In the body of the email, we're going to create the header of the table, and then include the Report Details token, formatted as HTML, within the table (remember that token is full of formatted rows for the table).  The structure of the table will be like this:
          

         <table border="1" style="table-layout:fixed; width:1550; border-collapse:collapse;"><font size="2"><b><tr style="background-color:blue; color:white;"><td width="200">Process name</td><td width="500">Instance Name</td><td width="100">Started by</td><td width="100">Last updated</td><td width="125">Assigned to</td><td width="250">Current step</td><td width="100">Step start date</td><td width="100">Due date</td><td width="75">Instance ID</td></tr></b>%(Form Details#[ ]##"HTML"#)</font></table>
         

      2. The email body can include anything else you need above or below the table.

4. The end result is that each week (or whatever schedule you have set for the workflow) the users will receive an email with a table of the forms that met the search criteria.