I'm an American speaker, and I'm personally unfamiliar with any U.S. dialects with this pronunciation. (That doesn't mean they don't exist, just that I'm unaware of them. I could be profoundly ignorant!)
Personally, if I heard læʃt, I would guess the speaker was from the area sometimes referred to as "drunk":
> Palatalization of [s]
>
> Lester and Skousen (1974) first reported an alcohol-induced palatalization of the segment [s] in native speakers of English. In 1985, Pisoni also reported having seen instances of productions of [s] as [ʃ] in intoxicated speech (Chin & Pisoni, 1997, p. 1…