True, the lottery is gambling, but states with lotteries simply exempt their lotteries from the gambling laws. (It's good to be King!) Radio stations may carry advertising for state lotteries from their states and from contiguous states. Thus, a station in Georgia may carry state lottery ads and information from Florida, SC, TN, 'Bama & NC as well as from Georgia; but not from Kentucky or Mississippi. There is no Federal law that I know of which prohibits gambling, this is true, but interstate gambling using communications devices is illegal. This is why the gaming sites have been chased offshore. FCC rules and Federal law do prohibit stations from airing lotteries (gambling) and define this as any game of chance for which a prize of value is offered and for which participants are required to render consideration. Technically, church raffles, PTA casino nights and VFW drawings are all lotteries, and stations may not air information about them. I've had a few situations where I have had to explain this to people wanting to promote their raffles and contests on the station where I worked, and some of these otherwise reasonable people became quite ... unreasonable.
As I understand things, stations may carry horse races in states where such is legal. Although network television does carry the Kentucky Derby and there is mention of odds and payouts, I believe that this has been either dealt with by special legislation, or it is considered to be a news item since it is an event of national interest. Other sports broadcasts cover points spreads and such, but you never hear them mention actual betting on the final score.
Turkey shoots, home-run derbies, etc. are not considered lotteries, by the way, because winning them is a matter more of skill than of chance.