Query Auto-Completion (QAC) is a widely used feature in many domains, including web and eCommerce search, suggesting full queries based on a prefix typed by the user. QAC has been extensively studied in the literature in the recent years, and it has been consistently shown that adding personalization features can significantly improve the performance of QAC. In this work we propose a novel method for personalized QAC that uses lightweight embeddings learnt through fastText. We construct an embedding for the user context queries, which are the last few queries issued by the user. We also use the same model to get the embedding for the candidate queries to be ranked. We introduce ranking features that compute the distance between the candidate queries and the context queries in the embedding space. These features are then combined with other commonly used QAC ranking features to learn a ranking model. We apply our method to a large eCommerce search engine (eBay) and show that the ranker with our proposed feature significantly outperforms the baselines on all of the offline metrics measured, which includes Mean Reciprocal Rank (MRR), Success Rate (SR), Mean Average Precision (MAP), and Normalized Discounted Cumulative Gain (NDCG). Our baselines include the Most Popular Completion (MPC) model as well as a ranking model without our proposed features. The ranking model with the proposed features results in a $20-30\%$ improvement over the MPC model on all metrics. We obtain up to a $5\%$ improvement over the baseline ranking model for all the sessions, which goes up to about $10\%$ when we restrict to sessions that contain the user context. Moreover, our proposed features also significantly outperform text based personalization features studied in the literature before, and adding text based features on top of our proposed embedding based features results only in minor improvements.