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.