This solution in Pro is not as convenient as locking the statistics in ArcMAP but it works. My need is similar. I am using a DEM to delineate features with varying changes in elevation. I use the DRA zoomed in to an extent that I can see the features. Essentially the DRA is calculating the statistics of my extent on the fly to give the best fit range. You can achieve this manually for your extent or area by using the Calculate Statistics tool. Just input your raster, then click on the pencil icon next to Area of Interest. An editable polygon will appear in the tool. Click on that, and editing tool options appear. Next draw your polygon to the edges of your extent, area, or however you want to capture the statistics of your raster. Run the tool. When finished, your raster statistics will be re-defined. DRA will be off, and you may have to re-assign your stretch settings to get it to look when you were viewing with the DRA. Optionally, from here, you can click on the symbology tab to save the statistics, Options>Save as XML. To change the raster back, you have to run the Calculate Statistics again on the entire raster or mosaic. Then in the symbology tab, load your saved XML file in Options. Someone just posted this add-on. I'm going to give it a try. https://community.esri.com/people/jescuderoesri-co-esridist/blog/2019/12/27/lock-dra-option-arcgis-pro
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