How to make an internal hinged door harder to open
There are premade solutions for that situation, try searching the web for "toddler proof doorknob." Here's a random one from Target.

This one is designed for your style handle. Keep in mind that it will only work if the door handles turn independently. ie, can you open the door without moving the interior handle?

In a worst-case scenario you would need to replace the lever with a conventional round knob and place a childproof cage on one side. That's a simple project you can do on your own.