Final answer:
There is no information in the provided text snippets that relates to the characters Jamie and Landon or a promise made on the way home from Cecile's diner, suggesting that a relevant source would be required to answer correctly.
Step-by-step explanation:
The question references a situation where Jamie made Landon promise something on their way home from Cecile's diner. This scenario seems reminiscent of a plot point from a novel or film, particularly Nicholas Sparks' 'A Walk to Remember.' However, based on the provided text snippets, there is no clear evidence of a character named Jamie or Landon, nor a promise made related to Cecile's diner. The excerpts do not seem to relate to the question, and as such, it is not possible to provide an accurate answer to what Jamie made Landon promise. It may be that the question refers to a specific scene in a book or movie not covered in the provided text. To answer this appropriately, one would need to refer directly to the text or film in question.