How to get to Yogyakarta from Cemoro Lawang?

I haven't taken the exact route you have taken, but I had a similar problem as I had to go back from Lawang to Jakarta. (Because my passport was stolen in Lawang, so you might want to watch your belongings)

What I did (and what's probably the cheapest option), is to take a minibus to Probolinggo (if I remember correctly, they run at least every 1 or 2 hours). The minibuses depart from the town, just ask around and people will be able to tell you from where.

Once in Probolinggo you should go to the bus terminal. From there I'm pretty sure there'll be regular bus services to Yogyakarta. I went there spontaneously, because the trains run quite infrequently and asked around at the travel offices there and some guy managed to put me on a bus to Jakarta (which if I remember correctly passed through Yogyakarta and was overnight) in a matter of 20 minutes or so. You should definitely ask around and not just wait as some buses might just be passing (coming from Bali) and not necessarily stop at the bus terminal but outside on the street.

Note that timetables probably won't be much use as there's different companies running the buses and as timetables seem to be rather decorative in Indonesia. I think you have the best shot by just going there and ask, in the worst case you might have to wait for an hour or two.

Also be prepared to negotiate for the price. I think I did get ripped off (If I remember correctly 600k Rupiah for 26 hours of bus), but at that time I was just very desperate to get to Jakarta before the immigration office closes down for Friday prayer.