You may use Search: list.
Using this request returns a collection of search results that match the query parameters that you have specified in the API request. Add part=snippet in your request since this is a required parameter. Then, you may add the following optional parameters with their corresponding values in your HTTP request:
channelId=[channelId] - to search resources created by a particular channel.
type=video - to retrieve a particular type of resource
eventType=live - to return only active broadcasts. Please note that if you use eventType, also set the type parameter's value to video.
Combining all of these parameters, you may send HTTP request using the following format:
https://www.googleapis.com/youtube/v3/search?part=snippet&channelId=UCXswCcAMb5bvEUIDEzXFGYg&type=video&eventType=live
To better filter your search, you may also opt to add more parameters that are listed in supported parameters.
Lastly, solution in this related SO post - How to check if YouTube channel is streaming live might also help.