I never feed my lantana and they are doing great I cut them back hard after the last frost and they always come back great I don't know if this is what your supposed to do but it works for me. My hibiscus froze this winter but they were in full sun and did well.
Hope this helps

I'm not sure why your lantanas aren't flowering. What kind do you have? I have both trailing lantana and bush lantana and they all flower like crazy. I do fertilize them occasionally..like in the spring with something like Miracle Gro Bloom Buster. They bush type look nice all year long. The trailing ones look kind of scraggly in the winter but perk back up in the summer.I cut them all back around January.
I sometimes get some yellow leaves on my hibiscus that are in full sun...especially in the summer when it gets really hot. The two that I have that are in partial shade stay greener. Over the years I have lost a couple of hibiscus after they suddenly wilted. I sill don't know why. One day they seemed to be fine and the next day they were completely wilted. Do not give them more water if they aren't dry.They do not like wet feet.

CP, seems like different types of lantanas seem to flower at different times. i have trailing purple ones that are blooming now and will slow down when the heat really hits. then i have golden yellow lantanas that are not blooming yet, but bloom like crazy all summer when it is hot. i also cut mine way back when the threat of frost is over and i usually only give them miricle grow once or twice a year. they seem to be able to take a fair amount of neglect and come back just as happy as ever.

You might check your watering just to make sure. If you are using drip irrigation with one or two gallon-per-hour emitters, you should run your system for at least two hours each time you water. This pushes the water deep into the soil and encourages deep roots. For established lantana (in the ground at least 1 year) you only need to apply water once every two weeks or so. As the weather warms up water more often - about once per week in the summer.

Here is a link to guidelines for watering landscape plants.

Here is a link that might be useful: Landscape Watering Guidelines