“Lazy Dog Pose” is one for the yoga therapy tool box, especially for hip osteoarthritis sufferers who can use it to postpone their need for surgery..
Another pose that can create release in the afflicted hip is this elevated lunge position:

If you can work with a helper, the following pose can offer relief:

When I had double hip surgery about 1-1/2 years ago, my practice of yoga had managed to forestall the operation for many years. And then, when I did have the operation, I was pain free almost directly afterwards, with not much need for pain killers. The progression from walker to wrist crutches happened within days, and by 18 days, I walked without a stick., Six days in hospital and 12 days in rehab with the physiotherapsit, got me into the the best condition for returning home, where I continued with my rehab exercises for 3 months. Gradually I became able to bring various yoga poses through my practice, very gradually.
Anyone who wishes to hold off surgery for as long as possible, the above exercise, are good to build strength and to encourage flexibility, and they just feel good!