you can lock as soon as they say ok, even without papers. I have refied several time in last 1.5 years just by calling, saying i do not want to pay a dime, what rate will you quote and agreeing on the spot or not, and locking. I usually pay .1 to .2 above the going rate, but have no out of pocket so I just see a lower payment.
I noticed GE too, is there any news pending?