Is singer Lady Gaga trans gender?

Since androgyny means (from dictionary.com): having both masculine and feminine characteristics. Having an ambiguous sexual identity. Neither clearly masculine nor clearly feminine in appearance, then yes, she appears sometimes masculine, and sometimes feminine, and sometimes completely androgynous. That is the definition of the Word.

If you meant a hermaphrodite, then no. She's not a person with both sets of genitalia. Completely different meaning.