Is there a way to lock an assignment after the due date so that students don't complete it late?

The short answer is that the only way to do this is to delete the assignment, but then you lose your data. Is there a reason you do not want them to complete the assignment? I use Khan Academy for homework as well. Mine is due by Friday at 11:59 pm. When I run the progress report, I use the time stamp to note any student who completed the work after the due date. 

Hi John

I have two reasons I'd like to share for why I have done a no-late-acceptance policy in some teaching environments.

1. Critically thinking and devious students may realize that they have the option of submitting things late as acceptable, even though it can only be an exception for a classroom that wants to maintain good learning standards. This realization is dangerous as it will manifest into action which will reinforce the idea they can use their critical thinking to get away with staying behind, instead of the ideal use, to get ahead. The wasting of their precious critical thinking skills leads to destruction of work ethic, which is higher as an indicator of academic and career success than IQ, will have the added bonus of a spread to the consistent working but less critically thinking or less devious students. It's also a pain in the rear for the teacher, confrere, and society who inevitably inherits their students.

2. In larger classes, it can be tedious to keep track of and extend assignments as exceptions, and emotionally taxing to remove points from a student who did complete their work.

Thus you may opt to say No late assignments, and may leave it at that or give some leeway like - only your top "insert number here" assignments, will be recorded for your grade, others will be dropped at the end of the semester. - This way students are less likely to submit late work knowing that they will get a zero if they don't submit on time, but also it doesn't tax you emotionally as a teacher because you know that you gave a fair safety net for an oopsie.