Explainer / John
John 20:28
Thomas answered and said to him, My Lord and my God.
ἀπεκρίθη Θωμᾶς καὶ εἶπεν αὐτῷ· Ὁ κύριός μου καὶ ὁ θεός μου.
What we did
We kept the ASV's wording, in modern English ("said to him" for "said unto him").
Why
The rendering is exact
Ὁ κύριός μου καὶ ὁ θεός μου is word for word "the Lord of me and the God of me," which English says as "my Lord and my God."
The grammar
Both nouns have the article and are in the nominative.
More
A nominative with the article is used for direct address in the New Testament, and "said to him" (εἶπεν αὐτῷ) names the one Thomas speaks to. English needs no added words to show this.
"Lord."
κύριος here is not a quotation of the Divine Name from the Tanakh, so the ASV's "Lord" is kept, as elsewhere in such cases.