Stack Overflow (SO) is extensively used by developers to resolve programming challenges. However, navigating numerous posts to find relevant answers is time-consuming. Recent research suggests summarizing SO post answers into concise summaries to quickly assess their relevance and quality. Existing approaches to this problem, though yielding promising results, predominantly employ information retrieval techniques or utilize pre-trained models to identify and extract salient sentences for summaries. Typically, these studies consider sentences in isolation, overlooking both the contextual relationships with neighboring sentences and the connection between the answer and the input query, thereby diminishing the effectiveness of the summarizer. This work introduces LASSO as an effective approach for summarizing Stack Overflow post answers. Our contributions are twofold. Firstly, we focus on extracting the contextual relationships between sentences to determine their salience in contributing to the summary. This involves using a BERT encoder combined with Long Short-Term Memory (LSTM) models, ensuring that the final representation of each sentence captures both its inherent semantics and the contextual information from the entire answer. Empirical evaluations and a human study demonstrate that LASSO outperforms established baselines by producing more concise summaries of Stack Overflow post answers. Secondly, we enhance the state-of-the-art dataset for Stack Overflow post summarization by introducing an additional dataset, which has been shown to improve the performance of baseline models, thereby advancing research in sentence-level summarization of various textual software artifacts.