Do not disturb the roots or cut it back till springtime unless you want it to die. The Lantana has hollow stems and if/when they fill with rainwater, the roots will rot. Spring time is the time to trim the dead canes. Yes, I believe your green growth is Lantana but it will probably be nipped back before winter ends. If you aren't sure if it is Lantana, you can rub a leaf and will know by the telltale fragrance.
I always cut one of mine back as it is a monster. One is moderately behaved and I prune only to control the growth over the walkway. The third one is a trailing Lantana which I leave intact until it tries to take over.
I suspect the blooms or lack of was due to weather. Good light is necessary but I have never fertilized my Lantana.
