What camera are you using?
Are you shooting raw files or JPGs?
What are your input sharpening settings in each program?
What are your output sharpening settings in each program?
Can you show us a matching example from both programs?
I have the same question
why does capture one render images sharper then Lightroom?
Because the two programs are different. They use different algorithms, and different default values. They have different underlying concepts of what a rendered RAW image should look like. They were not designed to produce the same results.
If you don't like the sharpness of the default rendering by Lightroom, change the default to be more to your liking.