In lightroom, is there a way to create a preset where a brush is automatically run? Example: If I make multiple different brush adjustments on an image, and I want the exact same edit on another image, can I create a preset for that?
No, brush adjustments are not saved in develop presets. Here are 3 options
1 If you want ALL the brush adjustments you can just copy/paste the brush settings.
2 If you just want a subset of the brush strokes you can create a virtual copy of the brushed image, remove the brushes you don't want and use that to copy/paste to the other images.
3 If you know you want to do the same brush adjustment on multiple images you can use autosync and brush the most selected photo and it will apply to all the other selected images.
Lr does not (natively) support saving brushes in presets, but it's a UI limitation, not an "under the hood" problem.
You can add brush strokes (or spot removals, or .. ) to a preset using a script I wrote (and offer for free), called
'Add Spots Or Paint To Preset'