My car isn't an Eclipse, but I thought you might be able to answer a question. I have the extended warranty but the car dealership won't take a look at my problem unless I pay up first then IF it is covered they will refund me. BS! I have a ticking under the hood. A lifter I think. Might be carbon build up or might need to replace the lifter. Some days it goes away after the engine is really warmed up (about 30 min of driving) and other days it's always there. Drives me crazy! What should I do or should I even be worried about it? I also need to replace the timing belt they say. I have 71K on the car. Otherwise it's in good condition and hasn't given me any problems. 

If your ticking problem gets quieter as the engine warms up, you're probably correct in assuming its a lifter issue. If it is a lifter(s) making the noise, it really will not cause any problems, but it is extrememly annoying. I had this happen on one of my cars. A few things you can try are using a slightly thicker weight engine oil, (example: if you're using 5W-30, try using 10W-30), you can have the lifters removed and cleaned, or you can do research to find if there are updated lifters with larger oil passages that are used to address the ticking problem in your particular car. In my case, I found new lifters with larger passages that eliminated my problem. But a good cleaning will also eliminate the problem for a while.

You're not causing any problems letting the lifters continue to tick, but I agree, it can get on your nerves. So you can try one of the avenues I listed to try to cure the problem, or just turn up the volume on your radio until the ticking subsides ;-)
Good luck!