“My fiancé obtained U.S. citizenship and returned to Ireland to live. When we marry, will I be eligible for U.S. citizenship? If so, how would I go about securing this for myself (and any possible future children)?
“I won a green card in the Morrison visa lottery, worked in America a few years, and then returned home. My green card expired a few years ago. Would this adversely affect matters?”
After you marry, you will not be immediately eligible for U.S. citizenship. First your husband would have to apply for permanent resident status (a green card) on your behalf. Three years after the status is granted, you would eligible to apply for U.S. citizenship.
The above is contingent on you and your husband maintaining a primary residence in the U.S., and adhering to the rules about keeping green cards valid – i.e., filing U.S. tax returns. If your post-marriage plans do not include residing in the U.S., then there’s no point in filing for a green card.
Your past Morrison visa won’t affect any future green card application. Many people obtain green cards, live in the U.S. for a few years and return to their home countries. This in and of itself is not a bar to future admissibility to the U.S.