How to get rid of this icon on my lock screen?

Go to Settings → General → Handoff & Suggested Apps and disable Installed Apps under Suggested Apps. This removes suggested apps from both the Lock screen and app switcher — it's not possible to disable one without the other.

The above option in @grgarside's reply isn't available on my iPhone - this option must have been removed in iOS 10.3.3, which is what I am running. The only option I could see was this one:

Go to Settings > General > Handoff and then turn Handoff OFF.
Worked for me on an iPhone SE running iOS 10.3.3

At first this seemed to work, but it hasn't completely stopped icons from appearing on the lock screen. However, turning off the Siri App suggestions, as mentioned by Jaime, does seem to have resolved this issue for me.

Suggested apps based on your location must be deactivated by disabling the Siri Suggested Apps widget on the Notification Center.

This guide explains how to do it:

First, swipe right on your home screen to access the widgets screen.

Scroll to the bottom of the widgets and tap “Edit”.

On the Add Widgets panel, locate Siri App Suggestions and tap the red minus.

Finally, tap “Remove”.

If app suggestions don’t immediately disappear, you may want to restart your iPhone.

This will not disable the Handoff functionality (the ability to continue doing the task where you left on our Mac), which will show an icon on the exact same spot. To disable that as well you must disable Handoff altogether.

I’m on iOS 11.0