Lavandula angustifolia, English lavender, has the purest and best fragrance, in my opinion. Variants ('Munstead' and 'Hidcote') are commonly sold at garden shops.

Lavender likes cool germination temperatures. Try sprouting in cells or flats indoors ... or you may need to buy plants.

You might try winter-sowing your lavender. I've had really fantastic results using this method -- got almost 100% germination.

Here is a link that might be useful: Winter Sowing Forum - lavender

l.augustifolia is "true" lavender. Lady lavenda is a hybrid. I started my lavender in my greenhouse...augustifolia slow to germinate and not good %, but once it's in a pot and transplanted it does well.
Lady lavenda germinated well, transplanted well. also blooms first year and has a nice fragrance.

Lavender does not like to be soggy. Would guess your soil is sandy, so it probably drains well, also, is not a good high humidity plant. Raised beds may be a good option, too.

Once established, it all grows well here in Ohio.
Let us know what happens.

I should mention I got excellent indoor germination of L. angustifolia by sprouting in cell packs under a standard humidity dome and fluorescent lights, with 1/8" (3 mm) holes drilled in the top of the dome to keep heat from building up. Because of the holes I had to mist with water every day or two. I still removed the dome for an hour every day to air out the trays. Germination took about 3 weeks (compared to 2-7 days for most annual herbs and veggies).