Male FLOTUS

[J. J.]

I don't believe "Second Lady" is too commonly used.  Al Gore's future ex-wife complained, humorously, that in introductions it was:

"The President of the United States, the First Lady, the Vice President of the United States, and Tipper Gore."

First Lady/Gentleman is more of a social title, technically informal.  Even a social letter would be address as:

The President and Mrs. Obama