I'd start the dill right now. Probably indoors where it will be warmer to germinate, then plant it out. It should provide you with dill foliage and when it gets too hot for it, the plant will bolt and go to seed. Never have figured out how to make dill and cucumbers deliver at the same time. lol
I grew borage last year as a bee attractant and it was lovely but required a bit more water than I could provide. It did last long enough to bloom though. Most herbal plants with larger or lush leaves will demand more moisture. That includes plants like basil and lemon balm.
Not sure how I managed but this was the first year I succeeded in keeping pineapple sage alive through summer and now winter. I did have it in ground but dug it last fall to provide winter protection.
This was also the first year that lavender has not died when it got hot. I have read it needs dry conditions but the roots need to be cooler. If you mulch it with white rock, it will reflect light onto the plant but will also reflect heat away from the soil/roots. Mine has looked a bit ill but is now putting on new growth and that was with minimal watering but we did have lots of humidity last summer.
If you research, you will find some types are better suited to the southern herb garden. I am sorry to say I do not recall which one I grew this year. My favorite herbal reference book is called Southern Herb Gardening. The mother/daughter team that wrote it lived just north of Houston. Let me look and see if they have a recommendation on lavender.