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- typeparameter'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.