LBlock is a lightweight block cipher proposed in ACNS 2011. It has a 64-bit block size and 80-bit key size which is the typical parameter setting accepted by most of the recent proposed lightweight block ciphers. It has fast hardware implementation efficiency and it still remains rather secure considering the recent results and the security margin it provides. In this paper, we investigate the differential behavior of the cipher in detail and propose (multiple) differential attack and boomerang attack against it. We are able to construct 15-round multiple differential paths which can lead to 17-round attack with complexity as low as 267.52. Also 16-round boomerang distinguisher can be build which leads us to 18-round boomerang (rectangle) attack with complexity 270.8473. These are the best differential attacks for LBlock in the single key scenario, which helps us understanding the differential behavior of the cipher.