As far as I can see, it relates to this working paper (dated March '09) (PDF) (via the New York Times's Economix blog) [I'm currently unable to find a more recent version].
After reading the paper, it does appear that the Sun is mainly correct in how it reports the study, even though it doesn't mention that winning the Lottery has no significant effect on a person's general health status (para 5.1, p. 15).
I do however, have two main issues:
- It names people whose lives have become "tragic" due to winning it. Leaving aside potential invasions of privacy that may cause, this implies that the paper also mentions them, even though it doesn't: the data is based on people's self-reported health from before their win and after it and a comparison is done (p. 6-11);
- It states that they suffer from long-term health problems, implying that winning the Lottery causes them, even though the paper states that winning it has no effect on these (para 5.3, p. 17)