The gemara in Nedarim 50 (and many other places) discusses how various rabbis refused to benefit at all from miracles, turning down gold and jewels, warehouses of grain, etc.
In the gemara, finding buried treasure is somehow classified as miraculous, even though it was already in existence prior to that point. That it occurred to rabbi Gamda was part of the miracle. This suggests that "naturally occurring phenomena" still fall under the rubric of miracles when sufficiently unlikely, akin to Maimonides' general interpretation of the miraculous being a confluence of natural phenomena occurring in just the right manner at the exact time needed.
The probability of winning is deliberately engineered to be in one to several hundred million (175 million for the powerball, ~259 million for the mega-millions). If we take this attitude toward miracles to be an optimal level of behavior, would the long odds on winning preclude such individuals from accepting lottery jackpot winnings as the product/benefit of a miracle?