Thanks for the updated patch, but I'm not sure FileInput class needs a islastline() method. I couldn't find any similar or duplicate feature requests on the tracker after this opened in 2004 (which is a sign that the need for this method is low.)

Also, the patch needs some work. Some comments:

* There is no documentation changes to Doc/library/fileinput.rst
* 'mark' is unused in Lib/fileinput.py
* Not sure why we need 't1 = t2 = t3 = None' in tests
* We could use self.addCleanup() instead of 'try...finally'
* fileinput.islastline() is not tested. We could reuse Test_fileinput_isfirstline.

According to commit history of Lib/fileinput.py, Serhiy has done a lot of work in the past few years. I just added him to nosy list to get his feedback.