I think the reply from frfernan is your best bet. To add to that:

You need not code an exact date, You can do like

SELECT lr.*

FROM lab_results lr

,patient pat

WHERE lr.patient_id = pat.patient_id and lr.sample_date >=

case datediff(month,pat.start_Date, getdate())

when 0 then lr.sample_date +1

when 1 then dateadd(month,datediff(month,0,getdate())-6,0) --- or dateadd(month, -6, getdate()) ...based on your exact requirement

else DATEADD(month, DATEDIFF(month, 0, pat.start), 0)

END

Plus it is more readable and you dont have to worry about patients with tests going back years or when January is the current month like you do with your initial approach.

Mark