It depends on the level of protection you want, but no, there isn't really a good way to do it with Wordpress. You can paywall a portion of your Wordpress site, but a live stream isn't going to go over HTTP, it is going to run over an RTMP stream or something similar. Paywalling your Wordpress site will make people pay to find out the name of the RTMP stream, but unless you have some type of authentication on the RTMP stream (or give each user a unique stream link), then you couldn't prevent sharing the link once one person pays.
What you really need is a stream server that provides either login to a stream (and only allows each user to access it once) or you need a stream server that can provide the same stream to multiple URIs and only allow one connection per URI. Both of these effectively do the same thing, they make it so that the connection details provided to a customer only work for that customer.
Alternately, you could use a list of authorized IP addresses and have your website add the IP addresses of paid customers as authorized viewers so that they can access the stream from their location. In this case, you should automatically update the IP address list whenever they log in.