Dialog participants sometimes align their linguistic styles, e.g., they use the same words and syntactic constructions as their interlocutors. We propose to investigate the notion of lexico-semantic alignment: to what extent do speakers convey the same meaning when they use the same words? We design measures of lexico-semantic alignment relying on contextualized word representations. We show that they reflect interesting semantic differences between the two sides of a debate and that they can assist in the task of debate’s winner prediction.