SQL Server 2022

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SnapshotDate	PartNum	LeadTime	OrderQty
2022-01-01	A	15	0
2022-01-01	B	10	1
2022-02-01	A	15	1
2022-02-01	B	10	0
2022-03-01	A	15	5
2022-03-01	B	10	3

/*
IMPORTANT ASSUMPTION: The combination of SnapshotDate and PartNum is unique.
*/

--4. Finally do a 1 to 1 Join back onto your orginal dataset, to include the total and the lookback date.
SELECT inp.PartNum
	, inp.SnapshotDate
	, subq2.LookbackDate
	, inp.LeadTime
	, inp.OrderQty
	, subq2.OrderQtyInLastLeadManyDays
FROM #InputData inp
INNER JOIN (
	--3. Sum the order quantity for each snapshot date, lookback date and part num.
	SELECT subq.SnapshotDate
		, subq.LookbackDate
		, subq.PartNum
		, SUM(inp.OrderQty) AS OrderQtyInLastLeadManyDays
	FROM #InputData inp
	INNER JOIN(
		--1. lets create the lookback date from the SnapshotDate and the LeadTime
		SELECT SnapshotDate
			, DATEADD(DAY, -LeadTime, SnapshotDate) AS LookbackDate
			, PartNum
			, OrderQty
		FROM #InputData
		) subq
		--2.Join the data set onto itself, where the SnapshotDate is within the date range (LookbackDate, SnapshotDate). Also make sure PartNum is the same...
		--I've chosen not to be inclusive on both ends (like a BETWEEN), as it didn't feel right. But you can easily change this if you wish.
		ON inp.SnapshotDate > subq.LookbackDate AND inp.SnapshotDate <= subq.SnapshotDate
			AND inp.PartNum = subq.PartNum
	GROUP BY subq.SnapshotDate
		, subq.LookbackDate
		, subq.PartNum
	) subq2
	ON inp.SnapshotDate = subq2.SnapshotDate
		AND inp.PartNum = subq2.PartNum
ORDER BY inp.SnapshotDate ASC
	, inp.PartNum ASC;

PartNum	SnapshotDate	LookbackDate	LeadTime	OrderQty	OrderQtyInLastLeadManyDays
A	2022-01-01	2021-12-17	15	0	0
B	2022-01-01	2021-12-22	10	1	1
A	2022-02-01	2022-01-17	15	1	1
B	2022-02-01	2022-01-22	10	0	0
A	2022-03-01	2022-02-14	15	5	5
B	2022-03-01	2022-02-19	10	3	3