In trying to figure out how to close his state’s expected budget gap, New Hampshire governor John Lynch is considering the addition of a fantasy-style game to the state lottery.

According to New Hampshire Public Radio, those familiar with the proposal — details of which have yet to go public — believe the game could deliver as much as $25 million in revenue for the state in fiscal year 2011.

It is believed that the game would work along the lines of what Montana rolled out back in 2008, allowing participants to select their players on a lottery ticket and then score according to real-game performance.

Montana has reportedly collected just $750,000 in sales from its NFL- and NASCAR-based games in two years of existence. The reason that New Hampshire’s projections dwarf that number is that the state would seek to offer it’s game online — enabling non-residents to take part as well. Montana’s fantasy lottery, on the other hand, is open only to folks in Montana (pop. 974,989, as of 2009).

New Hampshire’s primary obstacle here could be federal law. Whereas Montana was grandfathered into exemption (along with three other states) from the federal ban on sports gambling, New Hampshire is among the 46 that are restricted. This obviously doesn’t mean the state has to skip out on any fantasy plans, but it does mean that such a game would have to adhere to the specific carveout in the Unlawful Internet Gambling Enforcement Act that keeps fantasy sports payouts legal.

Should New Hampshire decide to head down this road and launch such a fantasy contest, it would likely replicate the daily and weekly formats that have been exploding in popularity throughout the fantasy sports industry over the past couple of years. In addition, it would obviously present a draw for sports fans throughout the state and beyond.

We all know that in a typical lottery game, you either pick some numbers or let a machine do it for you and then sit back and hope that your 1-in-a-trillion shot pops out of some machine filled with air, ping pong balls and disappointment. In the fantasy contest, knowledge of the sport at play would provide an inherent advantage over many other entrants, and payouts could be quite large (according to the highway lottery billboards).

FSB.com will keep you posted on any further developments we come across with this story.