It's hard to say. You have to tell us WHICH PART of the photos you are worried about. So far, I see lath and plaster (is that horsehair?) coated in white stuff that looks like paint. Which product are you concerned about?

How old is this stuff? Is this a floor, a wall, a ceiling? It is possible the paint has lead in it...but the rest of it is too hard to tell. You can always send samples away to a lab to have tested. Each section that you are worried about needs it's own sample. Each test costs $75 - $100 and is well worth the price.

Certain eras had HIGH asbestos use...other eras not so much. How old is this place?

This is a wall in my laundry room. I'm renting so I'm not sure how old the house is, I tried to find out online and it says about 1920. It just looks odd to me, it might be horsehair. It's my landlords that should be figuring this out, they just haven't gotten back to me about whether or not it was tested when they bought the house.

If you are asking about the hair in the plaster it's more than likely horsehair. Asbestos was used in lots of things but the fibers are different from what you are showing.

Why would your landlords have had it tested? It's not required most places.

Any idea about this wall? Really need to know. Thanks.

If YOU are concerned, then YOU pay to have it tested. Simple. And not even expensive.