The preview (pre-release) version of Microsoft Edge for iOS has been updated to version 42.6.1 which includes the ability to open Edge from your iPhone lock screen using Siri shortcuts.
You can use this functionality by creating a command like "Hey Siri, Open Edge" on the Siri Shortcuts app.
Additionally, you now have an option which lets you start from where you last left off, or start on a new tab.
The update also updates the browser widget, allowing you to get to quick actions and top sites from your Today screen.
In order to install the preview version of Microsoft Edge for iOS, you will need to request an invite from Microsoft, then follow the instructions Microsoft will send out and install TestFlight for iOS before you can setup and test out the app.
If you would rather wait for this version of Edge to be released publicly, you can install the current version 42.5.3 from the Apple App store by following the link below.