Your question asks if buying a lottery ticket is some form of questioning Gd's ability to help you through "normal" means. This would imply that you believe that buying a lottery ticket is NOT a normal means of acquiring money.
I would like to question that assumption. It is true, that most people do not win money from the lottery. And that would make this an "abnormal" way of acquiring money from the perspective of the average population. However, from the perspective of faith in Gd, a lottery is really no different than praying to find lots of money from some other means.
You can pray to Gd all day that he allows you to find a hidden treasure. However, if you don't leave your house and search for that treasure you will never find it. This is true for all forms of gaining money. If you pray to Gd to give you a good business prospect, you must then go out and conduct business, else you will not receive that reward.
In other words, your question here could easily be, "Is searching for gifts or treasures, a a lack of faith?", or somebody else might ask, "Is working for a living, a lack of faith?" Any one of the numerous ways to gain money could be singled out, as different from the other ways of making money, and thus would be open to the question if the activity is a lack of faith. In the end, all action which normally produces money is a question of lack of faith.
There are two resolutions to this problem:
- You argue that since the other actions are not a lack of faith, then buying a lottery ticket is also no a lack of faith.
- Every action appears to be a lack of faith, and we ask what is the proper action.
Jewish tradition takes route 2 and asks in many different ways, what is needed from a person to act and what will be the method of receiving a reward.
In general, we follow the dictum that if we make the opening of a needle, then Gd will create an opening for us large enough to drive a camel through it. This phrase originally appears within the context of Teshuvah, but has been used throughout the generations as a general way of understanding Gd's working in this world.
If you want a blessing of money, you need to open up needle eyes. Buying a lottery ticket is one of many ways of doing that. However, on the other side of the spectrum, we are told that the greater the effort, the greater the reward. And in that vein, since buying a lottery ticket requires little effort, one can expect little reward, unless the need is truly great.