Language models are often used as the backbone of modern dialogue systems. These models are pre-trained on large amounts of written fluent language. Repetition is typically penalised when evaluating language model generations. However, it is a key component of dialogue. Humans use local and partner specific repetitions; these are preferred by human users and lead to more successful communication in dialogue. In this study, we evaluate (a) whether language models produce human-like levels of repetition in dialogue, and (b) what are the processing mechanisms related to lexical re-use they use during comprehension. We believe that such joint analysis of model production and comprehension behaviour can inform the development of cognitively inspired dialogue generation systems.