What does it mean when a man has a dodgy past? It means he has skeletons in his closet.
What does it mean when a man likes Lana Del Rey better than Ed Sheeran? It means he has a closet full of women's leather pants (but no women in their dating history).
The first part plays on the idiom 'skeletons in the closet,' meaning hidden secrets. The second part makes fun of a guy's taste in music and implies he has unconventional taste and possibly a lack of dating experience, using women's leather pants as a symbol of that.