Crop lock keeps locking on its own

Others have reported flakiness with the lock icon:

https://feedback.photoshop.com/conversations/lightroom-classic/lightroom-classic-v10-padlock-symbol-in-crop-tool-shows-incorrectly-as-unlocked-when-aspect-crop-behaves-as-locked/5f9485c2bd2550489fc11a5a

Please add details of your issue to the bug report, and be sure to click Like and Follow at the bottom of the first post. That will make it a little more likely that Adobe will prioritize a fix, and you'll be notified when the bug's status changes.

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I can't reproduce what you describe. 

In your post what you describe sounds like you are cropping One image. You start the Crop Tool, Click the Crop Lock icon to Unlock it and when you Click on the image and start to Drag the crop the Lock Re-enables all by itself. Is that what is happening on your system?

If it is I suggest you Reset the LrC preference and if you have the GPU option enabled disable that too. Then Restart your computer and open LrC and Test.

Start the crop tool, immediately switch off the lock (which sets the default for next time), then crop the image.

Now start crop again with a different image and you'll find that the lock is disabled by default.