p.1 #2Lightroom - Deleted Images - A Way to Restore Edits?
To the best of my knowledge only if you have a recent catalog backup. When you delete images the catalog will remove existing metadata (this includes edits) and all generated previews. My approach is that when I am doing significant updates or major housekeeping I may generate a backup daily, otherwise I do it once a week.
p.1 #4Lightroom - Deleted Images - A Way to Restore Edits?
I've done this a few times by accident. I would go to a backup and either restore the old sidecar XMP file (if you use those) or open up the catalog backup that Lightroom makes by default.
Also, I think LR *might* remember the edits if you add back the file (import) with the exact same name in the exact same spot without doing any database optimization. I seem to recall this happening before but it might be a bug (and not intended behavior).