I assume you are using XMP files with Camera Raw. You can do that with Lightroom if you choose the option to write changes to XMP sidecar files in your Lightroom preferences. But if you use a Lightroom with its default setup the adjustments you make are stored immediately in the catalog. You can stop and close Lightroom at any point, and when you return Lightroom will retrieve from the catalog all the adjustments you have made to whatever image you have highlighted in the develop module, or in the library module as far as that goes. I have chosen not to use XMP sidecar files, and rely on my catalog to store all of my Lightroom adjustments. Again, making an adjustment in Lightroom creates a history step in the catalog immediately. There's no need to export in order to keep all of your adjustments.
Incidentally, regardless of how you set up your workflow, you cannot make "destructive" edits using Lightroom. Your master images always remain unmodified as far as the file contents are concerned.
I think your understanding of what Done was doing isn't right.
Clicking Done in ACR is doing NON-destructive edits and is analogous to what LR does as you make adjustments except in LR there is no Done button because the adjustments are applied immediately as you make them.
Save Image in ACR is analogous to File / Export in LR as both are making new images with the adjustments "baked in".