We purchased a used car from a dealership and went to trade it in only to find the car fax shows it as a dealer buy back/lemon.

Yes, they probably did need to disclose that. Having the car branded as a lemon will obviously affect the value of the vehicle, as I'm sure you just found out. I suggest that you contact a consumer attorney, whether its my office or another, for a more in depth consultation. You likely will not have any out of pocket legal fees to pursue a claim like this.