B737-800 pilot reported hearing a noise during taxi which resulted in replacement of both main gear tires.

Narrative

During taxi out a vibration was felt and a sound that felt like running over runway lights. It was subtle; but enough to raise our suspicions as we were not running over lights. Out of an abundance of caution; we coordinated with ATC for a spot to wait to coordinate with maintenance. We asked maintenance for an inspection who called an ops vehicle who confirmed a tire looked low. I asked which one; but could not get an answer. They specifically said we were ok to taxi back to the gate as it was low and not flat. We coordinated with dispatch and operations for a gate return. FAs and passengers were notified. Upon arrival at the gate; maintenance confirmed that both left main tires were low/deflated. They elected to change both tires.The sound and vibration was more subtle than I would've thought a dual flat tire scenario would be. It could've easily been overlooked. I am very happy we took the conservative route as both tires were very low and the inboard left main was seized and very hard to remove. Im not sure the specifics; but maintenance had to remove the brake with the tire. Now; 3 hours later; they are still working on it.