will using Round Up to kill lariope damage nearby plants (azaleas, red maples, etc?
RoundUp's main ingredient is glyphosate, which is sold in many other common products. Glyphosate is a "total vegetation killer", meaning it will be absorbed and damage any plant it contacts.
Glyphosate is also a "systemic" herbicide, meaning it is absorbed into the system of the plant--it does not just injure the exterior. It travels through the entire plant and, it's most valuable trait is that it can travel down and kill the roots.
When sprayed on only the thick bark of a mature tree, it may not penetrate through the bark. But it can damage thin-skinned or younger tree bark.