LSA is for analyzing relationships between a set of documents and the terms they contain, so it is not exactly for capturing sentiment values per se. You can use it to find related documents and then your algorithm sometimes finds unrelated ones or misses some completely, etc. And then the Precision, Recall and F measure come in.
Technically, LSA is a dimensionality reduction technique applied to vectors of term frequencies, often after tf-idf normalization. It transforms document content into latent topics space of a much smaller dimension.
LSA can be used as a preprocessing step for actual classification (performed with Naive Bayes, SVM, neural networks or whatever), which in turn can yield precision, recall, and F-measure.
However, it can't be guaranteed that LSA can extract sentiment in a way similar to a topic. It depends probably on the statistical distribution of words used to express positive and negative opinions in input documents.