In this sentence, should the is be a was?
On April 13, 2009, Lugo admitted he is the father of a child conceived with Viviana Carrillo.
Boofus McGoofus got this right. I am just going to expand on his answer. The heuristic rule taught to ESL learners is that the past tense should be used for indirect quotations, as in
Indirect quotation form:
But, this rule doesn't have to be applied in the case that the situation is still true, so is can be used. However, in a sentence like
"is" would be a little strange because both Lugo and his child are long since gone. So basically the heuristic rule can be broken in the case that the quoted fact is still true.
I would prefer "is" unless he has stopped being the father sometime since conception. While the child was conceived, he is the father.
Regarding the style, it depends on the focus
Is he the father of a child?
then the information in the sentence says only when that information was revealed
The question people asked three years ago was whether Lugo was the father of a child or not.
If the focus is in the present, you use the present tense, if it is in the past, you use the past tense.
I would use "he was the father" if the story speaks about the dilemma and all the problems around the time related to him being or not being a father. For example:
The entire passage is in the past. The key event is in the past. The dilemma was in the past: "was he or wasn't he the father?", so is the the answer: he revealed that he was.
(However, the language tests usually have no focus to decide about. It is not uncommon to find that you are mistaken in the test because you do not know the way your teacher or school likes to think. In this particular example it is very easy to justify using either the present or past tense unless more of the surrounding story is revealed.)