Q.How Much Lime Should You Give Tomatoes If They Have Tomato Rot?
And should I mix it into the soil or just put it on top of the soil?

Certified GKH Gardening Expert
Unless your soil is lacking in calcium, and that is rare, you don't need to add any lime. A soil test would definitely show if you need lime in your soil. If you wanted to add a little anyway, you could lightly mix it in around the plants. However, blossom end rot is usually a watering problem. From here on out, consistently water your plants and only at ground level. Do not wet the foliage.
They need about an inch of water a week. Blossom end rot usually just affects the first round of tomatoes, so the ones coming up should be fine. Here is more:
https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-blossom-rot.htm
https://www.canr.msu.edu/resources/blossom_end_rot_tip_sheet
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/applying-calcium-nitrate-for-ber.htm