What does a lid do?
A good lid broadens the applications of the pan it fits, turning a sear and saute-friendly stovetop skillet into a compact braising machine: a snug-fitting lid maintains a steady temperature, and traps steam to cook proteins and vegetables with wet heat. Where a partially covered releases steam during cooking, the closed system created by a tightly-sealed lid causes that moisture to condense as water droplets on the underside of the lid. That condensation then drips back down to the cooking surface, where the moisture is reabsorbed and continues the braising process.
But most simple lids have a key design flaw: a smooth, domed lid of any material will trap moisture, but the curvature of the lid will make water drip toward the outer edges of the pan — away from the center of the cooking surface, where proteins most in need of moisture are likely to be.