A couple of comments:

1) there is no guarantee that the update is acting on a single record. What should happen if your subquery returns more than one record?

2)in the second update you set the field to a constant based on a table join. The subquery is expensive in terms of time and probably unnecessary

It might be better to calculate the result first then update in one step. This might work

DECLARE @result float
-- if you are certain there is only one record per condition (primary 
+key constraints or something
-- you can omit this statement and the IF..ELSE block

/*
SET @result = (SELECT COUNT(*) 
               FROM   Calculation  D INNER JOIN Lookup_table L ON 
                        D.SUM_xi = L.SUM_xi
               WHERE  (D.SUM_xi < 13) AND (D.Key_m = @Count_me));
*/
-- try this instead
SET @result = (SELECT COUNT(*) 
               FROM   Calculation D
               WHERE  (D.SUM_xi < 13) AND (D.Key_m = @Count_me));

IF(@result = 1) begin
    SET @result = (SELECT D.SUM_wixi + SQRT(D.SUM_wi2xi / D.SUM_xi) * 
+(L.c - L.SUM_xi)
                   FROM   Calculation  D INNER JOIN Lookup_table L ON 
                            D.SUM_xi = L.SUM_xi
                   WHERE  (D.SUM_xi < 13) AND (D.Key_m = @Count_me));

    UPDATE Calculation
        SET Lower_95 = @result,
            Lower_95_Calc_method = 'UPDATE'
    WHERE SUM_xi < 13 AND Key_m = @Count_me;

    SET @Count_me = @Count_me + 1;
end
ELSE begin
  -- do something here to indicate multiple or zero records returned
end
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Update: I just noticed the WHERE condition doesn't require Lookup_table. You could simplify the query to a select on Calculation only. It will save you some time on the lookup. You could even incorporate the lookup back into your original query (but then you would lose some error checking)