Here is how I see the difference according to my current knowledge in Kotlin.
First one:
var myObject1 : Any? = null
Here myObject1 is a property that is nullable. That means you can assign null to it.
Second one:
lateinit var myObject2 : Any
Here myObject2 is a non-null property. That means you cannot assign null to it. Usually if a property is non-null you have to initialize it at the declaration. But adding the keyword lateinit allows you to postpone the initialization. If you try to access the lateinit property before initializing it then you get an exception.
In short the main difference is that myObject1 is a nullable and myObject2 is a non-null. The keyword lateinit provide you a convenience mechanism to allow a non-null property to be initialize at a later time rather than initializing it at the declaration.
For more info check this.