Lactate buildup might occur in the diaphragm and intercostal muscles during intense aerobic exercise with fast, heavy breathing. Not sure how it would occur in the abdomen unless we're doing intense core work -- sit ups, that sort of thing. But referred pain can be tricky and it's probably possible to feel pain from intercostal muscles and the diaphragm elsewhere in the torso.

Ditto, the adductor muscles in the upper thigh and lower core. That could conceivably build up lactate during a hard, prolonged effort. It could feel like it's in the gut.

The body uses built-up lactate as fuel, so when you ease up a bit to recover and the pain diminishes, you may indeed be building up and then using lactate.