In addition to customizing the content/display of the Timesheet with Custom Settings, you can also add custom fields.

Step 1: Add Field to T&E Item

In Setup > Create > Objects locate T&E Item and add a new Custom Field.
Note that it should be editable (i.e. not a Formula).

Step 2: Add Field to Field Sets

In the Custom Object T&E Item Entry, locate the Field Sets section.

Edit the Entry_Timesheet entry: Drag the Field(s) you want to add to the In the Field Set section.

Example: create a custom field "Line Item Activity" and added it to the layout.

Optional Step 3: Lookup Enhancements

If the custom field is a Lookup, the name of the record is displayed. You can add additional fields in the title or subtitle.

In addition to that, you can restrict the list of options to e.g. only active records and define parent record restrictions.

Example: Show only Opportunities, Cases, Contacts of the selected Account.

The parent relationship for the example above is provided, you can also use this for custom fields and relationships.

In contrast to the standard Salesforce lookup, you can view all options (e.g. without knowing come characters of the name).

For details see: Accorto Parameters