Are you asking whether watching puppies nurse can trigger a human female to let down milk? Yes, if it is someone who is still nursing a baby of her own, it is possible.
ROFL! Now that's a great new wrinkle to add to the old brain, eh? :-D
Speaking of menstrual cycles, I grew up in a small home with 2 parental units and 4 children and one bathroom. My father and brother would grit their teeth and wade thru the bathroom full of feminine supplies when my sister and I started "cycling." Naturally, mom, my sister, and I had to have our own particular brands of supplies, and there were times they nearly filled the bathroom.
Then there was my university experience with 4 girls sharing one bathroom. Same time, same station, every month. It really is true!
You'll never guess what I just stumbled upon...purely accidentally as I was looking at a writer's blog online the last hour....
Close emotional connection with a dog causes Oxytocin levels to rise. (Among other health benefits of owning a dog) Oxytocin levels influence lactation.
Well, gosh! I don't know. If I go a little metaphysical on you, please forgive me....
I suppose it's possible. If the moon can cause animals to ovulate, if sisters often have their periods at the same time, if men can have sympathetic labour pains....well anything can happen.
Where there is a strong bond, either between humans, or even between pets and their owners, then I would say -yes- one can influence the other in subtle ways beyond normal logic.