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The shrub appears to be Lantana camara, a different species from the lavendar trailing lantana. You will know for sure when it blooms in spring.
https://www.gardeningknowhow.com/ornamental/flowers/lantana/lantana-plants.htm

The tree appears to be a Palo verde or Palo brea, but I am unable to zoom in on the photo for detail.

http://www.amwua.org/plants/

There are many reasons for this finicky bloomer to fail bloomset. This article will help you to start narrowing down the possibilities: https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-not-blooming.htm

You will likely encounter one of two problems with your bougainvillea: lack of blooms or too-rapid growth. If the plant is not blooming, cut back on watering for a few weeks. They naturally bloom in the spring and seem to bloom harder in drier years. Bougainvillea needs to be trimmed to maintain its shape. However, be aware that bougainvillea flowers along its long branches so aggressive pruning of new growth will reduce bloom color. The best approach is to prune in the autumn after the growing season is complete so the plant will bloom from next season’s new growth.
Light: Full sun. Many growers move bougainvillea outside during the summer months.
Water: Keep evenly moist during the summer and nearly dry in winter. Bougainvillea blooms better with drier winter conditions.
Temperature: Relatively hardy. These plants are able to withstand tropical high temperatures and cold down to the mid-40s F. If you've moved your bougainvillea outside for the summer, keep an eye on falling nighttime temperatures in the autumn and bring it in if the temperature is expected to fall below 50 F. Likewise in the spring, be careful not to take it outside until nighttime temperatures warm up to around 50 F.
Soil: Well-drained potting mix with plenty of perlite.
Fertilizer: Feed your plant in the summer with weak liquid fertilizer weekly or use controlled-release fertilizer.

https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-winter-care.htm

As long as they are indoors, the timing of pruning is as important. The best thing would be to cut them back heavily after the blooms have dropped. They will not be picky about ferilizer, and an all-purpose will do just fine. As for watering... You will water them much less. Do not feed through the winter. Only water when the top of the soil dries completely.

Here is an article for more information: https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-winter-care.htm

Your area has 2 USDA climate zones. One of which this plant can survive outdoors, and one that is right below the growing zone for this plant. If you are able to, on the coldest nights you may want to bring it inside. Here is an article for more information: https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-garden-care.htm

This article will help:

https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-garden-care.htm