Battery Acid Dust Issue
It's very unlikely to be lead, smaller batteries don't use it. If the batteries were old rechargables they might contain cadmium (NiCd batteries). Most likely what you had was a disposable AA battery which will be an alkaline cell. As you'd guess, you can neutralise that with acid. But not a strong acid - you don't want to dissolve away the metal parts of the Lego battery box! 

There are a few how-to guides on the web that I found, like this one and this one They all suggest either lemon juice or vinegar as the acid, and focus mostly on 


don't touch the battery gunk with your hands (or eyes!)
wash it before scrubbing it as well as after
use something disposable to scrub it with
and don't touch it with your hands


Personally I'd put on rubber gloves, dump it into a plastic bucket full of water (always put chemicals into water, never water onto chemicals), swish it around and see whether the mess washes off. That's easy and you'll end up doing it anyway, so starting there might save you even having to find the vinegar bottle.