Air carrier Captain reported a loss of cabin pressure control during cruise. The crew made an immediate descent and landed at a nearby airport.

Narrative

While we were at cruise FL410 I felt my ears pop and felt pressure in my sinuses. The cabin altitude rate turned red and started to rapidly increase and continued to increase the cabin altitude surpassed 10;000 feet. My First Officer (FO) pulled the power back and prepared for an immediate decent. We donned our oxygen masks and performed the memory items then proceeded to request priority handling and ran the QRC decent checklist. In coordination with ATC we were cleared to 7;000 feet. Company was contacted and advised of our situation. We landed on Runway XX at ZZZ with no additional abnormalities. We did have passengers on board and passenger masks had deployed. When we had the masks on it was very hard to hear ATC and communicate. We did our best to coordinate all descents with ATC but did have to slow rate if decent as instructed by ATC initially. But; we believe they were able to clear all traffic below us and allowed us to decent to a safe altitude. We were over the lake and terrain was not an issue.