Stated preference (SP) surveys typically ask respondents to make a choice under a hypothetical situation. However, the choice context is often unrealistic, leading to errors and biases in the response. To overcome this, revealed preference (RP) data has been used to create a more realistic choice context for generating SP questions. For instance, in stated adaptation (SA) surveys, users are asked to answer SP questions based on a specific RP context they actually experienced. One challenge in SA surveys is that it is difficult for the respondents to precisely recall the RP context, especially when there is a longer time gap between RP behavior and SP response (response lag). However, no empirical studies have been conducted to test how elicited preferences vary in response to changes in the response lag. This study empirically examines the impact of response lag on SP responses using real-time SA survey data collected from Kumamoto and Hiroshima, Japan. To accomplish this, we developed a survey tool that enables respondents to answer SP questions in real time, i.e., immediately after their RP behavior. The empirical results confirmed that systematic bias increases with an increase in response lag. Additionally, the results showed that the greater the response lag, the more respondents tended to focus on the SP attributes rather than the RP attributes. These findings indicate that the timing of responses is an important survey design parameter when conducting a SA survey.