We design the first Leakage-Resilient Identity-Based Encryption (LR-IBE) systems from static assumptions in the standard model. We derive these schemes by applying a hash proof technique from Alwen et al.(Eurocrypt '10) to variants of the existing IBE schemes of Boneh-Boyen, Waters, and Lewko-Waters. As a result, we achieve leakage-resilience under the respective static assumptions of the original systems in the standard model, while also preserving the efficiency of the original schemes. Moreover, our results extend to the Bounded Retrieval Model (BRM), yielding the first regular and identity-based BRM encryption schemes from static assumptions in the standard model. The first LR-IBE system, based on Boneh-Boyen IBE, is only selectively secure under the simple Decisional Bilinear Diffie-Hellman assumption (DBDH), and serves as a stepping stone to our second fully secure construction. This construction is based on Waters IBE, and also relies on the simple DBDH. Finally, the third system is based on Lewko- Waters IBE, and achieves full security with shorter public parameters, but is based on three static assumptions related to composite order bilinear groups.