Hey, welcome to garden.org. I'm also in Florida and have tried year after year to grow lavender here. Sadly, in 15 years I have twice succeeded in growing a plant through the summer. They really don't like our high humidity and heavy rains. Most of the Mediterranean herbs have the same problem here - sage, thyme, oregano etc. also peter out for me. I think if I had a sunny window I could grow them indoors through the summer with the lower humidity in the house. But the sun is too high to get in the windows.
Rosemary is the only one that seems to survive pretty well.
Even though the native soil is fast draining sand, the roots still stay too wet, and most of the plants will peter out due to root rot. The only successes I had were by growing them in pots of cactus mix, and keeping them under an overhang of the house so they didn't get drenched with rain. I could more or less control the amount of water they got this way and allow the roots to get air, and dry out a bit between waterings.
The problem is almost certainly moisture related. You may even want to revise your planting to save your other plants. At a glance, I'd say the culprit is that mulch: in humid, high rainfall areas, organic mulch will hold too much moisture and rot the roots of dry loving plants. If your soil is fast draining, you could simply rake away that mulch and replace it with a bit of gravel or stone; light colored will reflect light and dry the foliage off. If your soil is too heavy, your best bet is to create a slightly raised bed with edging and ammend that soil with large grit.
