Letter of Recommendation Without Contact from the Student
I would do the "third thing" of nothing. You're not under any obligation to write letters of recommendation, and to me, the student's signing you up to do this is similar in principle to your department head signing you up for an extra committee assignment, or someone signing you up to volunteer for a public lecture, without discussing it with you first. I write this as someone who puts considerable time and effort into recommendation letters -- two that I care considerably about in the past 24 hours, for example.

Of course, it may well be the case that the student has no idea that writing a recommendation actually takes work, and it would be nice to contact him/her, but you've already tried the simple routes to this. I would devote my time to other tasks.