Does internal pressure of the lungs increase when the diaphragm pulls down?

Yes, when the diaphragm contracts and pulls down, it increases the volume of the thoracic cavity, which decreases the internal pressure of the lungs. This pressure drop allows air to flow into the lungs from the outside environment, facilitating inhalation. Thus, while the diaphragm's action decreases lung pressure relative to atmospheric pressure, it ultimately enables air entry into the lungs.