We present an in-depth analysis of data discovery in data lakes, focusing on table augmentation for given machine learning tasks. We analyze alternative methods used in the three main steps: retrieving joinable tables, merging information, and predicting with the resultant table. As data lakes, the paper uses YADL (Yet Another Data Lake) -- a novel dataset we developed as a tool for benchmarking this data discovery task -- and Open Data US, a well-referenced real data lake. Through systematic exploration on both lakes, our study outlines the importance of accurately retrieving join candidates and the efficiency of simple merging methods. We report new insights on the benefits of existing solutions and on their limitations, aiming at guiding future research in this space.