This page contains all the information you need on how to have a romance with Miranda Lawson.
Miranda is a romance option only available to Male Shepard if she surived the Suicide Mission at the end of Mass Effect 2. Your romance with Miranda is something that will build up over the course of the games. The first time you meet her is at the Normandy Dock: Bay D24 after the mission Priority: Palaven. During the conversation she’ll ask if she is going to be a part of Shepards plans and you’ll want to respond with “Nothing’s changed”.
Your next conversation with Miranda will be after the mission Priority: Citadel II. Here you’ll speak with Captain Anderson and he’ll give you Kai Leng’s dossier which you’ll want to read at your Private Terminal. Along with this you’ll also get another message from Miranda asking to meet her via the Spectre Terminal at the Citadel.
Some Point later in the game, Miranda will ask to meet you at the Presidium Commons. Here she’ll ask you for Alliance resources and you’ll want to respond with “I trust you”. As the conversation comes to a close, say “Stop talking and kiss me” to engage in an intimate moment with Miranda.