LBlock is a lightweight block cipher designed by Wu Wen-ling et al. in 2011. In this paper, a specific related-key differential is uesd to attack 19-round LBlock. The attack finds all the 80 bit keys in O(270.0) 19-round encryptions.The data complexity is 264 chosen plaintexts. Further more, a related-key impossible differential attack to 21-round Lblock is proposed. With 263 chosen plaintexts, the computing complexity of the attack is about O(271.5) 21-round encryptions for obtaining key.