Premier 1 Captain reported pressurization issues during takeoff resulting in two returns to the departure airport. A misaligned door lock was reportedly the cause of the issue.

Narrative

I was doing a flight to ZZZ2 carrying passengers. On the ground we have a pressurization test we complete before every flight to make sure the system is working. The test passed with no issues. We continued to the runway and took off Runway XX out of ZZZ with no appearing issues. We noticed the plane was a louder than normal at V1 so we continued takeoff as normal. At 2;000 feet we noticed the plane was substantially louder than normal and heard a lot of wind noise. I looked at the pressurization system and noticed we were not pressurizing at all in the climb. So I leveled the plane at 6;000 feet and slowed down to troubleshoot the issue. Nothing was working to get the system to pressurize. We took a small delayed vector north of ZZZ. Once that was completed we returned to ZZZ without further incident. On the ground I made phone calls to appropriate personnel to troubleshoot the issue. Maintenance arrived and seemed to have found the issue being the door wasn't sealing correctly due to a misaligned door lock. They made the adjustments; did the pressurization tests again with a successful pass. After the appropriate paperwork was filled out we went to takeoff again. After takeoff the system was working correctly at first; but through 5;000 feet MSL we lost pressurization again. This time with a very loud whistle. I checked the system again and the cabin altitude was climbing quickly. I made the immediate decision to return to ZZZ to prevent any further issues. After running the appropriate checklist we made a normal landing into ZZZ. Passengers de-boarded and I made the appropriate calls and wrote the discrepancy in our book again.