A certificateless encryption scheme from lattices is put forward by using preimage sampleable algorithm to extract partial private keys and learning with errors to generate secret values and public keys. The new scheme is indistinguishably secure against adaptive chosen-identity attacks, even against quantum-computing attacks. This is achieved in the random oracle model by formally demonstrating that this construction can fight against two types of adversaries who can request secret values. Proper parameter setting for the scheme is obtained specifically by performing an analysis of its correctness, security, and efficiency. Two methods for further improving its efficiency are used by enlarging its plaintext space according to both distinct approaches, which also shows that the given scheme is flexible. Specially, an efficient method of successive padding with fixed bit is presented for obtaining multiple longer bit strings determined by a fixed-size bit string, which provides a valuable contribution towards building the multi-bit certificateless encryption scheme. Due to advantages inheriting from lattices and certificateless cryptosystem, the proposed schemes are flexible, efficient, resistant to quantum-computing attacks and free from certificate management.