This happen because the Items is a collection of DataRow not a collection of strings.
To be able to remove a particular item you should work on the DataSource binded to the ListBox (the datatable)
Dim dt as DataTable = CType(lstRequired.DataSource, DataTable)
Using R = New IO.StreamReader(tFiles & "PlanExcluded.txt")
While (R.Peek() > -1)
Dim rows() = dt.Select("DocName = '" + r.ReadLine + "'")
For Each row in rows
row.Delete()
Next
dt.AcceptChanges()
End While
End Using
If your DocName data to remove contains a string with single quotes remember to double the single quote
Dim rows() = dt.Select("DocName = '" + r.ReadLine.Replace("'", "''") + "'")