So you did boil the mash and then added the lactobacillus after putting it in the fermenter. I'm trying to get this straight because there are different ways to sour a beer at different times in the beer making process. Also, I assume we are to understand you have not pitched yeast yet.
So if the 10.010 SG is actually 1.010, then bottle and keg it as is normal if the SG has been stable over a few days and your beer is clean enough for you.
It would seem that something got in there and fermented it out if you didn't pitch yeast. If you like the taste, consider yourself lucky. Most victims of wild yeast infections don't like the outcome from what I've read.
"Wild sugars?" was also a question for you. Did you mean wild yeast in your OP?