I used to buy my National Lottery tickets online in Britain.
It actually proved quite lucrative for me and Camelot even paid my winnings directly into my bank account for me.
I was surprised on moving to California to find that in the land of silicon valley I had to go to a convenience store to buy my lottery tickets. Not very convenient to buy that way nor check my tickets for winnings.
I would use an internet based lottery ticketing service if it were allowed in California.