Brand new All city Big Block, and sometimes when I push hard to accelerate from stop, it will feel like it jumped a gear/ slipped cog/crank. The slip is quiet, and the pedal drops about 5 inches. It does not happen all the time. I JUST got the bike to from the LBS. How to check for a loose lockring?

You cog wasn't tightened very well the first time, so it loosens every time you have used your legs to slow down and. Maybe get your own chainwhip and make sure the cog is really really tight. Then you tighten the lockring.

since I paid $563 for the bike cash, do you think the LBS should fix this for me free of charge since its only been 1 day? I noticed it happened on the first day when I got it home. I will be buying a chainwip, or do the rotafix. and lockring tool I should assume. But in the meantime, should I bring it? or maybe do it there? How much time does it take? probably 20 minutes??

The LBS should stand by their product and workmanship. Take it back to them ASAP and have them make it right before you damage something by riding it with loose parts.

1 Day? I would hope so. My LBS has a free inspection/adjustment policy. Bring the bike back after 30 days or 100 miles, and they will go over the bike and adjust for cables that have stretched and any other issue you may have FOC. Just took my Madone in since I had put 200+ miles on it already, and had some tweaking done. Guys at my LBS are really good.