First of all, have you had a soil test to determine what the pH of your soil is? Lime should never be added without doing so.

Second of all, I assume that you are using the term 'organic' to mean 'natural', 'pesticide free', etc. 'Organic' has more than one meaning and some folks interpret it differently.

If you are concerned with the need for calcium, but not an elevation of your pH, you might want to consider gypsum. It is a natural mined mineral (CaSO4), as is limestone (CaCO3). Gypsum provides calcium but because of the sulfur content of the product, the pH is not affected. IF you do need to lime your soil, you might want to consider dolomitic lime (CaMg(CO3)2) which also provides magnesium. Dolomite and plain lime come in pelletized forms, which is far easier to handle and apply. Again, these are mined minerals...perfectly acceptable in 'organic' gardening.

Hydrated lime (CaOH2) is not commonly used in gardening, and undergoes a process or two to convert the ground limestone to the hydrated form. It is very messy, fast acting, and should only be applied in fairly small amounts.

That lime at HD company name starts with a g?

For an organic garden you want ground limestone and that can be either calcitic limestone or dolomitic limestone depending on what a good, reliable soil test shows is needed.