Yes. You can use curl functions to call your REST API's.
e.g. curl.download.data() can be used to perform a GET request.
ret = curl.download.data("https://reqres.in/api/users/2",response.data,response)
|* response.data should now contain the JSON string for ID=2.
Similarly, you can perform POST request using curl.upload.data() or curl.upload.string(). I don't have sample with me, but probably, you will need to set headers for that. Play around with it and you will find a way.
Additionally, for SOAP webservice API's you can use soap.* functions provided by LN. And, for HTTP API's you can use http.* functions.
Also, you can write a JAVA/Python program to do all the API calling stuff and call those programs from LN using run.prog().
There are many ways, you just need to do decide how you would want to do it.
Hope that helps!