The size of the horizontal scrollbar is the first smell. I'd start by breaking down the CASE WHEN's into multiple lines:
SELECT
ROW_NUMBER() OVER(ORDER BY (CONVERT(varchar, effectivedate, 102)) ASC) Rn,
CONVERT(varchar, effectivedate, 102) effectivedate,
SUM(EuroCurrentBalance/1000000) TotalArrears,
SUM(CASE WHEN Multiplier > 2 THEN EuroCurrentBalance/1000000
ELSE 0
END) NPLs,
CASE WHEN ROW_NUMBER() OVER(ORDER BY (CONVERT(varchar, effectivedate, 102)) ASC) = 1 THEN 0
ELSE SUM(EuroCurrentBalance/1000000) - (LAG(SUM(EuroCurrentBalance/1000000),1,0) OVER (ORDER BY (CONVERT(varchar, effectivedate, 102))))
END MonthlyChange
FROM
DataWarehouse.dwa.FinanceMonthEndData
GROUP BY
CONVERT(varchar, effectivedate, 102)
GO
Note that you can group by effectivedate without doing the conversion again.
Then I'd look at the redundant pieces: EuroCurrentBalance/1000000 is repeated quite often, and CONVERT(varchar, effectivedate, 102) as well. Consider a subquery, or a CTE:
WITH PreSelectionCTE
AS
(
SELECT
CONVERT(varchar, effectivedate, 102) EffectiveDate,
EuroCurrentBalance/1000000 Arrear,
CASE WHEN Multiplier > 2 THEN EuroCurrentBalance/1000000
ELSE 0
END NPL
FROM
DataWarehouse.dwa.FinanceMonthEndData
)
SELECT
ROW_NUMBER() OVER(ORDER BY EffectiveDate) Rn,
SUM(Arrear) TotalArrears,
SUM(NPL) NPLs,
CASE WHEN ROW_NUMBER() OVER(ORDER BY (EffectiveDate)) = 1 THEN 0
ELSE SUM(Arrear) - (LAG(Arrear,1,0) OVER(ORDER BY EffectiveDate))
END MonthlyChange
FROM
PreSelectionCTE
GROUP BY
EffectiveDate
GO
This could probably be improved further, but at least it's much easier to read now! Note that ASC is implicit in an ORDER BY - I'd simply omit it, or specify it consistently: you have it explicit in 2 of your 3 ORDER BY's.