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There could be several things going on with lateral hip pain but often times what we see is that people are dealing with a tendinopathy issue, usually from overuse. A quick assessment you can try on yourself is to do a single leg stance and stand for 30 seconds. See if that aggravates the lateral hip. If so then it may indicate that the tendons of your lateral hip are a little hot.
First, I would recommend removing any movements or positions that aggravate the area. For example: take a break from Sumo DL and go to conventional, avoid stretching that brings the thigh across the body and hurdler stretch, in standing making sure you are not leaning towards one side putting more pressure on that hip, and even when sleeping avoid sleeping on the side where the aggravated hip is on top and dropped across the mid-line of the body. Tendons are good at handling tension but when they are hot they don’t do so well with compression. I think some light soft tissue work in the area from the TRS library is a good idea as well, just remember to focus on the breathing portion of the mobilization and don’t add so much pressure that you can’t sustain a deep breath. And just for now I would avoid stretches or movements that bring the thigh across the body. Main thing is to keep working in pain free positions and weed out the ones that flare it up.
Next, for your warm-ups I would try to work in some static holds to help with the pain and introduce some light load to the area. I would start with some mini squats with a 10 second pause using a Mark Bell Hip Circle around your knees 3-4x in your warm-up routine. We want to gradually increase the load to the tendon so eventually progress from 10sec holds, to 20sec, to 30sec, etc and see if that gets the ball rolling at all.
If you try tackling this issue yourself but still aren’t seeing any results or things are getting worse go ahead a seek out a pro. Nothing wrong with having someone check up on it. Just try to find a movement based physio, chiro, or sports doc who wants to get you moving and doesn’t simply recommend getting a cortisone shot and sitting on your butt for two weeks. Best of luck!