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