What do you mean? The lottery just gives you a green card. Once you have it, you can apply for naturalization in 5 years. Once you get your citizenship, you have pretty much all the rights and benefits as any other citizen, except you can't get elected president.
I was more referring to the big sudden surges part in that there is in fact a lottery acting to regulate the flow of migrants. I'd even go so far as to say that under many circumstances, a green card gets you many of the important rights and benefits as any US citizen (other than voting of course).