So, unfortunately I found out the hard way last night that deleting a livery from Showcase within the game
erases it from existence, while deleting it from your gallery simply removes it from the eyes of the general public...
I had just finished up taking some scapes pics for my Spoon Civic TC, so I shared them, then shared the style, as I'm trying to stick to a "3 pics, 1 livery" pattern on my gallery page. However I noticed that I forgot one of the Scapes pics, so I deleted the style, thinking it was removing it from my gallery, shared the scapes pic, then went to the livery editor to re-share the style again and get it into the order I wanted it. But then...
Then it dawned on me that it was gone. Erased. Deleted from the existence of time and space. It's like it never happened.
So now, I've had to start again... Luckily it's a fairly simple livery, but I've now got to track down all the decals I used in the first instance to as-closely match the old ones as I could. Because it was just about perfect!