I think the third one is the best.

All three are correct although I don't really like "stayed sleepless". It doesn't sound quite right to me. I would like to point out the differences between "sleepless", "lost sleep", "stayed up late" and "stayed up all night". "sleepless" tends to imply "inability to sleep" usually due to anxiety, nervousness or excitement. Example: "I couldn't sleep last night because I was told there would be a big surprise in the morning. It turned out that the 'surprise' was a new goldfish for our aquarium. Is THAT what I was sleepless for?" "to lose sleep" implies that you wanted to sleep but didn't. Example: "My son went out last night and didn't tell us where he was going or when he would come home. My wife and I lost sleep worrying about him." "stayed up late" means that you didn't go to sleep until late at night. It generally implies that you wanted to stay up late or had to stay up late. Example: "I had a big exam on Monday so I stayed up late Sunday night in order to study for it. I didn't go to bed until 2am." "stayed up all night" implies that you didn't go to sleep at all. Once again, the implication is that you wanted to or had to stay awake. Example: "I hadn't seen my friend for a year so we stayed up all night catching up with the details of our first year away from home."

They are all correct ...U can also say is this what I stayed up late for