Will I agree with this statement, the problem is that having/not having a lottery should be a state issue, not a religious one. The church's obvious influence on this topic once again shows the complete lack of speration of church and state in Utah.
The church has a lot of influence in Utah because (as Nate pointed out) many legislative positions are held by Mormons. They, just like anyone else, are going to do what they do according to their beliefs, and it is completely unreasonable to expect otherwise.
The implication that the State government is some sort of puppet of the LDS church is laughable. If this was the case, I'd imagine all the "fun" stuff (you know - alcohol, tobacco, R rated movies, bikinis, etc...) would be flat-out against the rules (think about how many "dry" counties there are in the United States - there are hundreds, in case you're wondering).
If your idea of separation of church and state is that anyone in an administrative position must divorce themselves from their beliefs, you need to study up a bit.