Put any outer (non-preserved) table references into the ON clause:

SELECT Employess.EmployeeID
FROM Employees
LEFT OUTER JOIN Timecards
ON Employees.EmployeeID = Timecards.lmpEmployeeID
 AND lmpTimecardDate = '20071024'
WHERE lmpEmployeeID is NULL ;

In addition to David's post, here is what is happening:

The FROM ... LEFT JOIN operators define a table that includes all rows
in the outer table, Employees in this case. This table includes the columns
from the Timecards table, but for the employees there there is no timecard,
all columns have NULL. Which you apparently have understood, since you
the condition "lmpEmployeeID IS NULL". But then there is a lapse, and you
filter lmpTimecardDate despite it is not likely that there is a row in
Timecards where the date is non-NULL and the employee ID is NULL. (At least
one would hope so!) Moving the date condition to the ON clause addresses
the issue, as it now will be part of the condition that builds the
table that is then filtered by WHERE.

Personally, I would prefer to write this query with NOT EXISTS:

   SELECT E.Employee
   FROM   Employees E
   WHERE  NOT EXISTS (SELECT *
                      FROM   Timecards T
                      WHERE  E.EmployeeID = T.lmpEmployeeID
                        AND  T.lmpTimecardDate = '20071014')

Simply because this clearly express what this is all about.

And I would also use a date format that is safe from misinterpretations.