I am in Amarillo, TX and have planted a few Red Valerian, Lantana and Catmint in a front sunny bed. The previous owners had installed weed barrier lining and then covered that in Lava Rock. When I planted these I move the lava rock, cut X's in the weed barrier and planted these. Now I'm thinking that the weed barrier material and the lava rock are not going to allow these plants to spread and thrive. Am I correct, and should I remove the rock and barrier and replace it with mulch?
You are correct. The barrier will prevent it from thriving as it should. You can keep the lava rock, as long as you take up the barrier. You can also mulch if you prefer, but the lava rock will be just fine.
There are a few of these plants which have randomly appeared
That is a Valerian plant! Here is an article that will help:
https://www.gardeningknowhow.com/edible/herbs/valerian/growing-jupiters-beard-plant.htm