I'm in the USA and I have tried to purchase tickets online but without a UK bank account and 'switch' card I could not complete the process. If you have those you should be OK.. Just google the UK National Lottery site , and follow the prompts to open an account. It will recognize that you are logging in from outside the UK and ask some questions about the legality of playing from the country you are in.
You can play foreign lotteries while in the US - you wouldn't want to claim the money here though if you are now a resident ( if you won) as Lottery winnings are taxable and I think they are not in the UK.

I had a feeling I had read something somewhere that said you couldn't so I googled it and found this link to an article on the bbc website

http://news.bbc.co.uk/1/hi/8190956.stm

You cannot do it. I have tried from Spain using Brothers UK address and my own UK debit card. Went through all the procedure but at the end it denies verification.

Thanks for your help everyone...why cant Camelot make it clear???????????....anyway I know what to do now....thanks again...Rod Smith