Based on the classification of organisms, a lion would share characteristics most similar to an animal in the same genus family class genre

All of the given options belong to the taxonomic rank. Each higher rank is characterized with more general characteristics of the animal. So, the lower the rank the more specific characteristics the animal share. 
Beginning from the lowest rank the taxonomic rank is the following: species, genus, family, order, class,phylum, kingdom, domain. Based on this classification of organisms, a lion would share characteristics most similar to an animal in the same genus.