Couple of ways I can see.

One, is at the dataset level, and insert your extra rows in there. Provided that the query is only for your report set, it's not a bad way to go, but it does look a little odd (at least to me). One way of achieve this is as follows (using LAG and a couple CTEs):
CREATE TABLE #Name (LastName varchar(20));

INSERT INTO #Name
VALUES
  ('Abbe'),
  ('Adams'),
  ('Arlyn'),
  ('Bird'),
  ('Bryn'),
  ('Burn'),
  ('Bzork'),
  ('Charlie');
GO

WITH Spaces AS
  (SELECT 1 AS BlankRow UNION ALL
  SELECT 2 AS BlankRow UNION ALL
  SELECT 3 AS BlankRow UNION ALL
  SELECT 4 AS BlankRow),
Lags AS (
  SELECT LastName,
         LAG(LEFT(LastName,1)) OVER (ORDER BY LastName) AS LastPersonInitial
  FROM #Name)
SELECT CASE WHEN Spaces.BlankRow = 4 OR Spaces.BlankRow IS NULL THEN LastName ELSE NULL END AS LastName  
FROM Lags
     LEFT JOIN Spaces ON LEFT(LastName, 1) != LastPersonInitial
ORDER BY Lags.LastName, BlankRow;
GO
DROP TABLE #Name; 

Another method would be to use grouping on your tablix on the report. I'm explaining this from memory right now, but if you know SSRS well enough, it should set you on the right path.

Firstly, add a group to your tablix on the LEFT most character of your Lastname Field. This will likely add a new column to your tablix on the left hand side. Leave it there for the moment. Right click the row in your tablix where your data is, and there will be an option to insert a new row inside the group. Do this 3 times (so you have 3 blank rows under your data row in your tablix). Then, select the new column that was made when you created the group and then right click it. Select Delete Column; this should present you with a dialogue window asking if you want to delete the column or the column and the group. Select just the column and click ok.

Now, when you Previous the report, it should put 3 blank rows between each group (the left most character). It will, also add 3 lines after the last group (if you have one, the group z), so you'll need to add some logic to hide those rows.

If you try the latter option, and you get stuck, let me know. I should be at a PC tomorrow with SSRS, so I'll be able to create a sample rdl and provide a copy (as well as post some more detailed steps). However, see how far you get first.