Is your agent a human being (or some other animal, as opposed to some artificial creature that has been created specifically to be rational? If it is, then you should distinguish between two different utilities of the same lottery when the drawing is in the future:

1) The expected utility after the drawing

2) The utility (actual, not expected) of having the drawing in your future

The second is influenced by the first, but also by the emotions and any other experiences that are caused by beliefs about the lottery. This post deals very well with the first, but ignores the second.