Validity affects the act, while liceity affects the 'legality' of the act. So if a baptism is invalid, then the baptism never occurred (i.e. one has not been baptized and needs to be baptized). So if a baptism is illicit, then it was not celebrated under the structures that the Catholic Church has defined (i.e. one has been baptized, but the Sacrament was not celebrated in a way directed/authorized by the Church or with the full approval of the Church).
Source: wiktionary