That depends on your soil.

Without a soil test there is no knowing.

Soil tests are free or very low cost through the county ag agents.

Why do you wnat to add lime?
Have you done a soil test to find out the PH?

Tomatoes and basils can thrive in wide range of PH
tomato : 5.5 to 7.5 (practically just about any soil)
basil: 5.5 to 6.5 (most garden soil)

Even if your soil ph is lower than 5.5or 6.0 (it is very unlikely) adding lime cannot change it instanly.
It will take months and you have to do it little bit at a time.
To increase PH(by adding lime ) and how much lime to be applied , depend on the soile type, less for sandy soil, more for clay, medium for loamy.

Lets just take loamy soil(average):

To increase PH by 0.5 you will need to add about 2 lbs of hydrated lime per 100 square yard (900 sqr-ft). To change PH by 1 unit, double that. But again, you should not do it in one shot.
The best time to add lime is in the fall or very early spring, to allow it to work.

So then you should not just blindly try to add lime.
Have a soil test done or get one of them $20. Ph tester at least (from HD) and check your soil PH yourself . It might not be as accurate as a lab test but it should give you a pretty good indication as where you stand.

If you live in an area where lawns are generally limed, limestone can be used in spring and fall by sprinkling to the point of making the soil surface look like the very beginning of a snowstorm. Probably a trowelful for your garden size. I have used it in the garden over 50 yrs this way. On LI dolomitic limestone will prevent magnesium defiency as well as supplying adequate calcium for tomatoes. A bag of limestone is cheap and enough and will last for many many years of liming a 4x8 plot.

My stepdad (old farmer dude lol) told me to sprinkle enough so that the soil looks like the powdered sugar on a doughnut). has worked for me!

I like the idea of snowstorm and donuts. That is what I've done in the past without any research, so I guess I'll continue.
One of these days I'll get to a soil test.

3/4 cup of lime per tomato plant will not hurt plant...sometimes to much dolomite lime can hurt because of high magnesium.....just use ag lime from co-op or feed store.
will supply all the calcium for one season that you need...mix in soil before planting