lavender can be grown hydroponically. I was surprised to learn this. Interesting.
I would think aeroponics would be better than kratky for this. Mainly because the roots would be exposed to more air with an aero tower, rather than constantly submerged like in Kratky. Although the plants will produce water roots that should tolerate it. As an experiment you can try to water root some cuttings of lavender if it works then Kratky should work too.
Lavender likes a lot of sun if you are growing this indoors I don't know if you can get enough light for it. Basil and Catnip will tolerate less light.
Happy gardening in Hawaii. Gardens are where people grow.