Dialect adapters that improve the performance of LLMs for NLU tasks on certain sociolects/dialects/national varieties ('dialects' for the sake of brevity) have been reported for encoder models. In this paper, we extend the idea of dialect adapters to decoder models in our architecture called LoRDD. Using MD-3, a publicly available dataset of word game-playing conversations between dialectal speakers, our task is Target Word Prediction (TWP) from a masked conversation. LoRDD combines task adapters and dialect adapters where the latter employ contrastive learning on pseudo-parallel conversations from MD-3. Our results for en-IN conversations on two models (Mistral and Gemma) show that LoRDD outperforms four baselines on TWP, while bridging the performance gap with en-US by 12% on word similarity and 25% on accuracy. The focused contribution of LoRDD is in its promise for dialect adaptation of decoder models.