Lithology identification plays an essential role in formation characterization and reservoir exploration. As an emerging technology, intelligent logging lithology identification has received great attention recently, which aims to infer the lithology type through the well-logging curves using machine-learning methods. However, the model trained on the interpreted logging data is not effective in predicting new exploration well due to the data distribution discrepancy. In this article, we aim to train a lithology identification model for the target well using a large amount of source-labeled logging data and a small amount of target-labeled data. The challenges of this task lie in three aspects: 1) the distribution misalignment; 2) the data divergence; and 3) the cost limitation. To solve these challenges, we propose a novel active adaptation for logging lithology identification (AALLI) framework that combines active learning (AL) and domain adaptation (DA). The contributions of this article are three-fold: 1) the domain-discrepancy problem in intelligent logging lithology identification is first investigated in this article, and a novel framework that incorporates AL and DA into lithology identification is proposed to handle the problem; 2) we design a discrepancy-based AL and pseudolabeling (PL) module and an instance importance weighting module to query the most uncertain target information and retain the most confident source information, which solves the challenges of cost limitation and distribution misalignment; and 3) we develop a reliability detecting module to improve the reliability of target pseudolabels, which, together with the discrepancy-based AL and PL module, solves the challenge of data divergence. Extensive experiments on three real-world well-logging datasets demonstrate the effectiveness of the proposed method compared to the baselines.