check out liriope

Something that will tolerate the light and moisture conditions that exist directly under a tree canopy.....typically some sort of groundcover but often shade loving annuals or things like hostas, ferns and liriope work as well, provided irrigation is available.

Lantana wants full sun.......that's why it didn't flower.

Lantana needs full sun to thrive. Any shade loving plants/flowers should do well. Any nursery will help you.

Personally I like the simpler look of nothing under trees: i.e., just let the grass grow as close as it can to the trunk; mulch if you feel it looks better close to the trunk where the grass doesn't grow. I'm getting older and I find this much easier to maintain - I can just mow the grow with the lawn mower and no need to edge. (I don't have mulch next to the trees because our ground is moist as is, and mulch would be carried away by rain into the grass.) Just my opinion though - its all what you like of course. Oh - and I've researched the issue of whether it is detrimental to the tree to have grass growing over its roots. Apparently only when the tree is very young. HTH.

In the situation asked about here taking out that edging, removing whatever loose filling material is present inside the edging and having the grass come as close as possible to the base of the tree would look better. For one thing it would give that part of the lawn a better shape. And also allow the nice flow of the paved path to stand out better.