Yes it is leaf spot.

The leaf spot spores are in the soil. This disease spreads by water splashing from the soil and the water with the spores splash onto the leaves. Then it spreads to other leaves again from water carrying the spores from leaf to leaf.

Pick off the worst leaves--all of them if you can but you don't want to denude a plant. Spread a fairly thick layer of mulch around the plant so the infected soil can't splash. When you water don't wet the plant. Treat with an fungicide for leaf spot. Garlic water and baking soda sprays might help.

Be prepared to fight this disease until the soil is sterilized either by solarizing it with plastic or until you have a prolonged hot dry spell. Don't plant suseptible plants in the same place next year