This will work:

IF OBJECT_ID(N'tempdb..#Visits') IS NOT NULL

DROP TABLE #Visits;

CREATE TABLE #Visits

([TargetID] [int] NOT NULL,

[TargetName] [nvarchar](255) NULL,

[Interaction] [nvarchar](15) NULL,

[Created] [datetime] NULL)

INSERT INTO #Visits

(TargetID, TargetName, Interaction, Created)

VALUES (1, 'abcd', 'target_acquired', '2012-10-03 20:24:00.000'),

(1, 'abcd', 'target_acquired', '2012-10-03 20:46:00.000'),

(1, 'abcd', 'target_lost', '2012-10-03 20:46:00.000'),

(1, 'abcd', 'target_acquired', '2012-10-03 20:47:00.000'),

(2, 'efgh', 'target_acquired', '2012-10-03 20:51:00.000'),

(2, 'efgh', 'target_lost', '2012-10-03 21:01:00.000');

SELECT V.TargetID,

V.Interaction,

MIN(V.Created) AS Created

FROM #Visits AS V

WHERE V.Interaction = 'target_acquired'

GROUP BY V.TargetID,

V.Interaction

UNION ALL

SELECT Losses.TargetID,

Losses.Interaction,

Losses.Created AS Lost

FROM #Visits AS Losses

WHERE Losses.Interaction = 'target_lost'

UNION ALL

SELECT Losses2.TargetID,

ReAquired.Interaction,

ReAquired.Created AS ReAquired

FROM #Visits AS Losses2

CROSS APPLY (SELECT TOP (1)

ReAquired.Created,

ReAquired.Interaction

FROM #Visits AS ReAquired

WHERE Losses2.TargetID = ReAcquired.TargetID

AND ReAcquired.Interaction = 'target_acquired'

AND ReAcquired.Created > Losses2.Created

ORDER BY ReAcquired.Created) AS ReAcquired

WHERE Losses2.Interaction = 'target_lost'

ORDER BY TargetID,

Created;

I added a row to the sample data so that it has a re-acquire in the sample. Does that do what you need?