This question is far too difficult to answer without knowing -- what agency do you work for, and what business does your LLC do? For example, if you are a letter carrier, and you own a landscape company, there is no conflict at all as long as you do your normal work. On the other hand, if you are a FBI agent responsible for arresting criminals and your business is defending criminals you are breaking the law.
On my profile there are several legal guides. I recommend reviewing the following which may be helpful to you:
Hiring a lawyer; Is it Legal? Is it Illegal?...Understanding the different court systems;
Legal terms used in litigation………………………………………………………..
LEGAL DISCLAIMER…………………………………………………………………..
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information about this issue.
Your agency's ethics officer should have information on your agency's policy regarding outside business interests. Also you should take a look at Part 2635 of Title 5 of the Code of Federal Regulations (5 CFR Part 2635), entitled STANDARDS OF ETHICAL CONDUCT FOR EMPLOYEES OF THE EXECUTIVE BRANCH. Section 2635.403 of that Part has government-wide guidance on "prohibited financial interests." There are specific examples in the section (taken I was told from real situations) that may be helpful. One thing you will read in that section is that there may be special rules for each agency, which reinforces the need to check with your agency's ethics regulations and your agency's ethics officer. It is my understanding that you can get a written determination on a specific question from the ethics officer if you request it.