There's nothing illegal about it: no laws even regarding a holster that I know of - it just has to be concealed.
However, two major points of concern:
1) The main point of a holster is to render a firearm inoperable by covering the trigger while the gun is being sat on, pushed/pulled into/out of pockets or clothing, or otherwise jostled around as you carry it. I don't think the LCP even has a safety, making covering the trigger that much more important. The obvious risk being something like a piece of clothing getting caught in the trigger guard as you attempt to push the holster in your clothes, etc. I would never use a holster like that as it's not much different and only arguably safer than Mexican carry. I think it's just a matter of time before a lawsuit puts that company out of business.
2) I make it a practice to avoid talking about firearms at work. All it takes is the wrong person overhearing, and they could go to management or HR to get the company's policy changed or enforced.