Before you can add expenses onto a timesheet, you must add the expense type to the Allowable Expenses tab on the placement.
From the timesheet
Click View in the top ribbon
Click Placement from the menu
If you cannot see the allowable expenses tab, click the three dots at the end of the tabs and select Allowable Expenses
Click the ✚ button
Fill in all the fields on the Placement Expenses pop up
Click Save
When you return to timesheets you should now be able to see the Invoice Line Item Code you added