Electronic Health Records present a valuable modality for driving personalized medicine, where treatment is tailored to fit individual-level differences. For this purpose, many data-driven machine learning and statistical models rely on the wealth of longitudinal EHRs to study patients' physiological and treatment effects. However, longitudinal EHRs tend to be sparse and highly missing, where missingness could also be informative and reflect the underlying patient's health status. Therefore, the success of data-driven models for personalized medicine highly depends on how the EHR data is represented from physiological data, treatments, and the missing values in the data. To this end, we propose a novel deep-learning model that learns the underlying patient dynamics over time across multivariate data to generate personalized realistic values conditioning on an individual's demographic characteristics and treatments. Our proposed model, IGNITE (Individualized GeNeration of Imputations in Time-series Electronic health records), utilises a conditional dual-variational autoencoder augmented with dual-stage attention to generate missing values for an individual. In IGNITE, we further propose a novel individualized missingness mask (IMM), which helps our model generate values based on the individual's observed data and missingness patterns. We further extend the use of IGNITE from imputing missingness to a personalized data synthesizer, where it generates missing EHRs that were never observed prior or even generates new patients for various applications. We validate our model on three large publicly available datasets and show that IGNITE outperforms state-of-the-art approaches in missing data reconstruction and task prediction.