I’ve created an animation on After Effects and exported as .json and upload it to my website via Elementor Pro Lottie Widget.
The question is:
I want to control the animation with a custom button or menu item, on click, on hovert etc.
Elementor Pro Lottie Widget doesn’t allow you to play the animation when you click a specific button. But you can play the If you click the animation, or on hover, either the animation, or a specific part of the layout. You can do this by using the Trigger option provided by the Elementor Widget. Have a look at this video on how to do that: How to Use Elementor's Lottie Widget [PRO] - YouTube
Even though the Lottie JS players allow you to control it with programatically, It might be a bit difficult to control the Lottie player provided by the Elementor widget.