Alexis Lockwood will do any crossword puzzle she comes across. She’ll pick them up in subways and doctor’s offices. And just about every night, she and her girlfriend Annie Barrow wind down before bed with a little puzzling.

So she didn’t suspect anything unusual when, Sunday morning while staying at their friends’ house in Washington D.C., Ms. Barrow said, “I found this crossword puzzle. Want to do it?”

She...