Lambda architecture is a novel event-driven serverless paradigm that allows companies to build scalable and reliable enterprise applications. As an attractive alternative to traditional service oriented architecture (SOA), Lambda architecture can be used in many use cases including BI tools, in-memory graph databases, OLAP, and streaming data processing. In practice, an important aim of Lambda's service providers is devising an efficient way to co-locate multiple Lambda functions with different attributes into a set of available computing resources. However, previous studies showed that consolidated workloads can compete fiercely for shared resources, resulting in severe performance variability/degradation. This paper proposes a resource allocation mechanism for a Lambda platform based on the model predictive control framework. Performance evaluation is carried out by comparing the proposed solution with multiple resource allocation heuristics, namely enhanced versions of spread and binpack, and best-effort approaches. Results confirm that the proposed controller increases the overall resource utilization by 37% on average and achieves a significant improvement in preventing QoS violation incidents compared to others.