For Lightwave:
They work with the usual suspects, practically the same as Heatmiser: https://lightwaverf.com/works-with-lightwave/
They offer a fully fledged API, but I didn’t find a way to use webhooks. So also not directly usable with Apilio: https://jsapi.apiary.io/apis/linkpluspublicapi/introduction/general.html
Since you use Alexa, it looks to me like this is the best (but still complicated) way, to somehow integrate it with Apilio. You can get webhooks to work with Alexa, but it’s only through some plug-ins and not easy to setup and maintain: Alternative to ifttt to integrate with alexa?