Addressee detection for dialog systems aims to detect which utterances are directed at the system, as opposed to someone else. An important means for classification is the lexical content of the utterance, and N-gram models have been shown to be effective for this task. In this paper we investigate whether neural networks can enhance lexical addressee detection, using data from a human-human-computer dialog system. Even though we find no improvement from simply replacing the standard Ngram LM with a neural-network LM as class likelihood estimators, improved classification accuracy can be obtained from a modified neural net model that learns distributed word representations in a first training phase, and is trained on the utterance classification task in a second phase. We obtain additional gains by combining the class likelihood estimation and classification training criteria in the second phase, and by combining multiple model architectures at the score level. Overall, we achieve over 2% absolute reduction in equal error rate over the N-gram model baseline of 27%.