Poor condition asbestos and rat infestation grounds to break lease?

Hello!

We are a little over three months into a lease in New York. Since we've moved in there have been a number of problems. House wasn't clean and smelled very strongly of dog urine, a garage that we were supposed to be able to use for my husband's art studio had a significant rat infestation which continues to be a problem (rat poop everywhere on boxes and art stretchers so we can't use or safely store stuff there without risking contamination and needing further cleaning). Due to the unusable garage we were instructed to use the basement which come to find has significant amounts of exposed (confirmed and tested) asbestos pipe wrapping that professionals confirm to be in poor condition. The washer and dryer and other belongings are also down there. We have spent a decent amount of time in the basement, my dogs have gone sniffing around down there and my toddler has also been down there. We communicated our concerns to the landlord over a month ago and while they say they are looking into remediation, no concrete steps have been confirmed. The landlord also mentioned during the phone call that a previous tenant expressed concern and thought it was fine as long as it wasn't touched. No asbestos was disclosed in the lease. We also told them over a week ago that we were going to start looking elsewhere. We don't feel comfortable or safe living here anymore and are going to break the lease. After a few lawyer consultations, it sounds like we have a right to legally end the lease but I'm reaching out here to learn about other's experiences or advice? What grounds or support would the landlord have in this situation?

Location: New York