MyQ lite was a groovy smartapp/device handler. While you could get the code directly from the developer, you would not be able to run it as ST is currently phasing out the legacy groovy platform. IDE is also being shut down and some features have already been terminated such as installing groovy smartapps/device handlers.
The reason the MyQ Edge uses an always on server is to create communiction between the ST hub and MyQ. The old MyQ Lite did that directly through the cloud but no longer viable on the new platform.
There is one other option if you don’t have an always on server to run the new Edge Myq and that is to use IFTTT. Not the best but it is an alternative option.