If you don't have to pay to get in then it's not a lottery. I suppose you could call it a contest, but there is nothing wagered like a lottery. I doubt any court would find otherwise.
You do not understand the legal definition of "consideration" in this context. You have to pay to buy the mining computer, and electricity to run it, which is your "entry fee" for the Bitcoin lottery. The value of that entry fee flows to "Bitcoin" as a "consideration" when you calculate a block to be added to its blockchain - a function vital to the continuation of Bitcoin. If Bitcoin used every single block generated by all miners, it would be "buying" a "service" and would be a business. Instead, a random chance function (leading zeros in the block) is used to award a prize to one single block winner every ten minutes. All other blocks generated by all other losers (which are cryptographically valid but lack the winning zeros) are discarded.
I know it's uncomfortable to acknowledge that Bitcoin mining is a lottery, but legally it is. Protests to the contrary, or silence so far on this point from State law enforcement or courts, are irrelevant. Favorable federal legal rulings so far from IRS or DOJ are also irrelevant, since gaming law is handled on a State level.
So far the States have yet to speak up on this point of law - Bitcoin as an illegal lottery. It will not be a good day for Bitcoin when they do.