Public Key Encryption with Keyword Search (PEKS) makes it possible for a cloud server (CS) to match a trapdoor and a ciphertext. However, with the upgrowth of quantum techniques, most of the existing PEKS schemes will be broken by quantum computers in the coming future. Moreover, they are also under the threat of potential key exposure. Lattice-based forward secure PEKS scheme (FS-PEKS) overcomes the two problems above by combining the techniques of forward security and lattice-based cryptography. However, FS-PEKS schemes work in public key infrastructure (PKI), which will incur complicated certificate management procedures. In this work, to overcome the key management issue but still guarantee security even when attackers corrupt the keys, we extend the FS-PEKS scheme into the identity-based framework and present a forward secure identity-based encryption with keyword search (FS-IBEKS) scheme from lattice. The proposed scheme is secured under the selective identity against chosen plai