Yes, if you're away from your iPhone with your Apple Watch, you should be able to use the ECG application, as long as you've already completed the initial setup with Health on your phone first.
I'm not sure if you mean with the LTE Apple Watch or just the GPS version - but I don't think it matters.
I did this. I turned off my iPhone and made sure my Apple Watch S4 GPS version was not connected to WiFi. I successfully ran an ECG. I turned my iPhone back on and was notified of this new reading.
Yes it works on LTE watch, but you will get a message before you start saying that the watch will not get calls or messages during the ECG. The watch has to shut down the cellular radio to do the ECG, it must affect the readings.