what kind of lawyer do I need to sue for slander and liable?

No way to tell because your question skips over he essence of defamation (untrue statements made with knowledge of the falsity)  in favor of just declaring the events defamatory. The practical issue, though, assuming that the statments were defamatory is whether or not you are willing to spend money on an attorney to address the issue, as very few competent lawyers will take defamation cases on a contingent fee (paid by prcentage of the damages recovered) because they are unlikely to actually getpaid for the work needed to sue and get a judgment and such claims are not usually covered by insurance. If not, you may want to focus on other means of addressin this type of issue as I have seen this exact circumstance become an obsessiv Hatfield and McCoy battle that bankrupts both parties. If you are commited to doing something about it, however, the first test of that commitment will be the sacrifices YOU make to gather the funds to actually hire legal counsel.