This paper presents ltzGLUE, the first Natural Language Understanding (NLU) benchmark for Luxembourgish (LTZ) based on the popular GLUE benchmark for English. Although NLU tasks are available for many European languages nowadays, LTZ is one of the official national languages that is often overlooked. We construct new tasks and reuse existing ones to introduce the first official NLU benchmark and accompanying evaluation of encoder models for the language. Our tasks include common natural language processing tasks in binary and multi-class classification settings, including named entity recognition, topic classification, and intent classification. We evaluate various pre-trained language models for LTZ to present an overview of the current capabilities of these models on the LTZ language.