If I have a recorded conversation of me and my wife's lover, in which he admits to having an affair with my wife, would it be enough to file a lawsuit?

I am sorry to hear about this.  I am sure this is painful.  What are you wanting to sue for?  If you are meaning filing for a divorce or dissolution of marriage, generally you do not need any reason to file to end your divorce.  You do not need proof of an affair to file to end your marriage.  If you are referring to suing the man your wife had an affair with over the affair, these are generally not sound cases to pursue.  Every once in a while there is a case such as this where a spouse prevails against the person their spouse had an affair with, but these cases are rare.  Suing someone is expensive, time consuming and emotionally draining.  You have to consider whether or not it is worth it to you.  Even on the off chance that you were to prevail in this case, what amount of money would make you whole again?  You also need to consider whether or not the individual has the assets to pay you if you were to prevail.  Often times in these cases, people end up spending quite a bit on court costs and attorneys fees and the case does not go anywhere.  If you really feel it is in your best interest to pursue this, I would suggest you talk with a family law attorney in your area and discuss the specifics of your situation.  Good luck to you.