Thai basil leaf spot problem
I had a similar problem, and it turned out to be caused by water droplets on te ;eaves/ Basil is an extremely sensitive plant and its leaves are easy to damage by mechanical means. The leaf may be burned by your gro lights on the outside edge.If there is an actual disease, you can look at the leaf under magnification to see if there are any fuzzy spores present. Otherwise I would switch to bottom watering only and make sure the gro light doesn't get too close to the plant.
I don't think it's downy mildew since I don't see powdery, light colored accumulations. The plants are not under grow lights but in a mostly north facing window. Today, I discarded the plants since they are dropping dead leaves and they just don't seem "normal", but I can't find a suitable description of the problem on line. thanks however for your response.
If you have a fungal infection, it moves quickly and you can see the raised spore producing structures with a magnifying glass. If you still have any live plant material, you can send samples to the Penn State plant clinic http://plantpath.psu.edu/facilities/plant-disease-clinic/instructions or take them to your local Penn State Extension.
Thank you again for your help. Jerry
Oh, that sounds like a great variety - suitable to our apartment with reasonable light, but also with some small LED grow light panels that I have. I agree, most basils are tricky with the leaf diseases or other sensitivities. So I'll give it another try w/ piccolino and see what happens, trying to clean up after the Thai basil problem. I decided they were far enough "gone" to throw them out (sadly). Thanks again for your help. Jerry