|MadSci Network: Biochemistry|
As a chef, you will know that the use of 'acidulated water' (ie water with some lemon juice in it) is often used to prevent the browning of the cut surfaces of fruit and vegetables such as potatoes, artichokes and avocados. That is because the enzyme which does this (polyphenol oxidase) does not work at low pH's and the acid of the lemon renders it out of action, so the oxygen in the air will have little or no effect on the cut surface.
So... lemons themselves will not go brown when cut open.
When stored in the fridge, my experience is that the lemon rapidly dries out so that the whole peel becomes hard, whilst the cut surface merely dries a little. If it is stored in a plastic bag, or covered with clingfilm, then something similar to what you report DOES happen.
This is caused by bacteria , which break down the cellulose in the lemon, so reducing the cut surface to a 'mush'. Fungi CAN grow on a lemon, but do so only very slowly and produce a different reaction - generally you can see the green spores of the Penicillium fungus and they do not, generally, produce any slime.
I hope that helps you - use the lemons up more quickly and don't cover the cut surfaces - I find them very useful to rub into my fingers after washing to remove any brown stains (broad beans, artichokes) or smells (onion or garlic)!
Try the links in the MadSci Library for more information on Biochemistry.