My advice is to first find out what it is possible to do without a laywer. I got a Green Card through the lottery and while I have heard of tons of others doing the same for thousands upon thousands of dollars in lawyers fees, I did it for about 60 cents in postage. The lawyers will always tell you they are necessary, but beware, because that may well be total bollocks

If you are a UK citizen then you cannot apply via the lottery. As mentioned though, if you had a Irish passport or if you happened to have been born in another country you could apply. I don't think you have anywhere near a 50% chance of winning the lottery, as many people try for years and years, but it is much more likely (though probably less profitable) than your local lotto

Anyhow, I am just rambling, and don't really have any direct info to help you sorry. Good luck!