Lexical Alignment is a phenomenon often found in human-human conversations, where the interlocutors converge during a conversation to use the same terms and phrases for the same underlying concepts. Alignment (linguistic) is a mechanism used by humans for better communication between interlocutors at various levels of linguistic knowledge and features, and one of them is lexical. The existing literature suggests that alignment has a significant role in communication between humans, and is also beneficial in human-agent communication. Various methods have been proposed in the past to measure lexical alignment in human-human conversations, and also to implement them in conversational agents. In this research, we carry out an analysis of the existing methods to measure lexical alignment and also dissect methods to implement it in a conversational agent for personalizing human-agent interactions. We propose a new set of criteria that such methods should meet and discuss the possible improvements that can be made to existing methods.