Ask the Expert: Planting Lavender

Hello,
I received a Spanish lavender plant in the mail as a gift.  It looked great when I got it, but after replanting it in a larger pot, slowly died despite a lot of attention (water, sun, etc.).  I’ve grown lavender before, but never had this much trouble (I live in a warm, Mediterranean climate, and it’s been fairly warm).  I kept the pot inside in a windy at first, then moved it outside thinking it needed more sun.
Could you please explain how best to transplant this replacement so that it  fares better?  I just used a regular potting soil mix before, and a larger terra cotta pot.
One thing that I think might be the culprit– there are some above-soil roots (I think)– should those be planted above or below the soil line in a new pot?

Thanks!  Photos are attached so you can see the roots I am describing.

Kami