It's not clear what was happening here. You say that you were applying for a government job, but you also say that you were tested by LexisNexis, which is a private business. You say that you want to sue LexisNexis, but your real concern is that you are permanently disqualified for state government jobs. I don't understand your facts well enough to answer this question. If you were applying for a government job, then there ought to be some way that you can make an administrative appeal. If there isn't, then you may have a due process claim of some sort. If you were applying for a job as a government contractor through LexisNexis, then you don't have a lot of rights, but the drug test shouldn't affect future applications with the government.
You need to talk to an employment lawyer and go through your specific circumstances.