Laser-induced breakdown spectroscopy (LIBS) is a popular, fast elemental analysis technique used to determine the chemical composition of target samples, such as in industrial analysis of metals or in space exploration. Recently, there has been a rise in the use of machine learning (ML) techniques for LIBS data processing. However, ML for LIBS is challenging as: (i) the predictive models must be lightweight since they need to be deployed in highly resource-constrained and battery-operated portable LIBS systems; and (ii) since these systems can be remote, the models must be able to self-adapt to any domain shift in input distributions which could be due to the lack of different types of inputs in training data or dynamic environmental/sensor noise. This on-device retraining of model should not only be fast but also unsupervised due to the absence of new labeled data in remote LIBS systems. We introduce a lightweight multi-layer perceptron (MLP) model for LIBS that can be adapted on-device without requiring labels for new input data. It shows 89.3% average accuracy during data streaming, and up to 2.1% better accuracy compared to an MLP model that does not support adaptation. Finally, we also characterize the inference and retraining performance of our model on Google Pixel2 phone.