What is the meaning of 躺着躺着?
According to this context, 说着说着 is correct to me. 昨天晚上我们在一起聊天，说着说着忽然停电了。 The hint is 聊天, so either 聊着聊着 or 说着说着 makes sense in the context. 

...着...着 means 'while (doing) ...'.