The promise of ultimate elasticity and operational simplicity of serverless computing has recently lead to an explosion of research in this area. In the context of data analytics, the concept sounds appealing, but due to the limitations of current offerings, there is no consensus yet on whether or not this approach is technically and economically viable. In this paper, we identify interactive data analytics on cold data as a use case where serverless computing excels. We design and implement Lambada, a system following a purely serverless architecture, in order to illustrate when and how serverless computing should be employed for data analytics. We propose several system components that overcome the previously known limitations inherent in the serverless paradigm as well as additional ones we identify in this work. We can show that, thanks to careful design, a serverless query processing system can be at the same time one order of magnitude faster and two orders of magnitude cheaper compared to commercial Query-as-a-Service systems, the only alternative with similar operational simplicity.