Yes. I didn't drill holes in mine for a while because I just left the lid off, resembling my larger sized cubic yard compost bins. However, using a lid with plenty of holes can offer the same benefits- good airflow and it allows rainwater to penetrate, too. Now that it's summer, compost systems need more moisture to work effectively... keep them damp, and if you want to use a lid, drill holes to contain the process without hampering it.
http://www.rodalesorganiclife.com/garden/how-to-build-compost-bin Check the link above for a semi-technical three-bin design that will result in the most hassle-free composting there is. If I had the space for a three-bin system, I'd be on it in an instant. In other words, when you work with large bins, there's much more room for error as opposed to a worm system or composting with a pair of trash cans. The only aspect of this design that I deviate from is the process itself- I don't turn compost at all, so I'd just keep the middle bin full of cover materials, add to the first bin for up to a year using cover materials from the middle bin, then work on the third bin when the first is at capacity.
https://www.youtube.com/watch?v=Xy417xt-bco If you're into turning your compost, this excellent video is for you. I'll pass!