Chaste Tree:
aka  Vitex Agnus-Costus 'Shoal Creek'

. . . is the closest look-alike to a LILAC that we're going to find that grows well here in FL: and it actually is quite fragrant and pretty!

Chaste tree is known as Vitex Agnus-Costus
and the cultivar called "Shoal Creek" is what we can get.
Native to southern Europe and central Asia.

Flowers are shaped like a lilac, is a purple color, very fragrant, and grows to 10-15' in this area.  Perfect for zones 6-9 --- we're in zone 9.

Vitex prefers loose, medium moisture, well-drained soils in nearly full sun. It is often grown as a multi-trunked, bushy shrub, but it can be also be shaped into a gorgeous tree.  If you want a tree, buy it already trained as a single trunk tree:  you won't win trying to re-shape even a 3g bush into a tree.

Vitex loves our warm winters (compared to zone 6) and is  EXTREMELY aromatic.   It attracts butterflies and bees  and has no serious insect or disease problems.   Expect it to lose all its leaves in the winter.

and here's the sizes available as of this writing:
7gal / $55 / 3-4' tall (about 2-2.5' wide)
15gal / $125 / 4'tall x 4'wide (trimmed size)
15gal / $145 / ~6'tall x 3' wide / single trunk