Probably not in this situation. Wouldn't you ALWAYS need to populate the dictionary at some point? I would rather wait a little bit longer when starting the program so it can populate a dictionary, then have the program seemingly hang when I am playing the game while it populates it lazily.
I think lazy initialization is better used when it is an expensive operation AND the data isn't always required. For example, hibernate might lazily load some of the fields of an entity object that aren't related to the entity's key because not every use case of the entity will need that part of the data, only the ones that explicitly ask for it.