I take lisinopril myself for HBP and have done so for decades. I've never used naproxen except maybe once or twice. One Rx that might possibly be of benefit for arthritis instead of naproxen is meloxicam, also known as Mobic. I use it occasionally with no ill effects to report.
Ugh, ya, it's a dilemma. I worry about blood pressure so think every time before I take an ibuprofen. But I don't have a chronic issue like arthritis. I would look for some alternatives if you need them. They are limited but there. Non steroidal anti inflammatory medications do have documented affects on the heart including raising blood pressure. They work so well for pain and immflamation that it is a real shame. Some will have more of an effect than others. To note, Mobic is also an Nsaid. But perhaps has less heart effect. Here's an article I found helpful
Tylenol? Tramadol? Physical therapy? Exercise? Those are on the list as potential options.
My suggestion is to discuss this with your doctor. Perhaps a trial without naproxen would work to let you know for sure if it is causing the issue. Let us know!