I am not a lawyer (IANAL),
But, I bet a zillion dollars you aren’t going to find a radio station that plays just LP. And it will be challenging to find one that doesn’t run ads or has a talking DJ. Actually I don’t think that exists, legally. As far as I am aware, streamers give up on the idea of playing mainstream music over their streams because of this. It might be better off to find indie music artists who aren’t represented by the RIAA and are okay with sharing. (you still have to ask them individually, but I imagine indies are far more willing to want the free representation from you).
Linkin Park has an iHeart radio station. It’s got talking though.
In addition, Last.fm, and other internet services have stations that, if you pay, you can make the ads go away. However they are radio stations and therefore don’t play LP only.
Also, pretty much any FM radio station nowadays has online streaming. Of course this will net you ads and DJ’s too. But they’re all there. Even your local one I bet.
I doubt Spotify and Grooveshark count because they’re not radio stations.