Lime helps to sweeten the soil IF it's already a bit acidic, here in UK, IF lime is required after testing the soil, we spread the GARDEN LIME late winter as we begin to prepare the soil for our planting early spring, I would NOT add lime to ground while food plants are already growing and remember it has to be GARDEN LIME not some stuff from the builders yard.
I would add the lime in winter IF the soil was cleared of all the edible plants BUT OK for things like Rhubarb as by then the top growth is underground.
By adding the lime in winter here in our climate, IF the weather changes and we cant dig the bed over to mix the lime into the soil, the cold, frost and rain will help get the lime down into the soil for you. In spring I dig the beds over and the lime will by then be well mixed in.
It is a huge mistake to over lime as Doug has said, you can alter the PH of your soil with lime, when adding it half way through the growing season, you could end up loosing your crop or altering the taste even.
Because lime is good for the soil (FOR CERTAIN VEG OR FLOWERS) it's a huge mistake to keep adding it without knowing the soil actually requires it.
Invest in a cheep soil testing kit (a few dollars from garden store) it will tell you the reading of the test AND what type of nutrients are required, so you would use that reading against what your carrots or peas require, much safer in the long run.
Kindest Regards. WeeNel.