Does it makes sense to use state pattern with vitual proxies?

class HeavyweightObjcet
{
    public void operate() {
        System.out.println("Operating...");
    }
}

class LazyInitializer
{
    HeavyweightObjcet objcet;

    public void operate()
    {
        if (objcet == null)
            objcet = new HeavyweightObjcet();
        objcet.operate();
    }
}

Here I'm making a virtual proxy for a heavyweight object. Each time before calling HeavyweightObject::operate, the program checks first whether the object is null or not. This part is checked once and only once through the entire lifetime of the object.

A possible improvement maybe using the state pattern like this:

class HeavyweightObjcet
{
    public void operate() {
        System.out.println("Operating...");
    }
}

class LazyInitializer
{
    HeavyweightObjcet objcet;
    State state = new UninitializedState(this);

    public void operate()
    {
        state.operate();
    }
}

abstract class State
{
    LazyInitializer initializer;

    public State(LazyInitializer initializer)
    {
        this.initializer = initializer;
    }

    abstract void operate();
}

class UninitializedState extends State
{
    public UninitializedState(LazyInitializer initializer) {
        super(initializer);
    }

    @Override
    public void operate() {
        initializer.objcet = new HeavyweightObjcet();
        initializer.state = new InitializedState(initializer);
        initializer.operate();
    }
}

class InitializedState extends State
{
    public InitializedState(LazyInitializer initializer) {
        super(initializer);
    }

    @Override
    public void operate() {
        initializer.objcet.operate();
    }
}

Does this solution make sense?

Is there any possible improvement to the code?

Are there any examples to something like this that's done before?

Is it an unnecessary complication or does it worth it or does it depend on the situation?

Does it make the code faster? I mean, the extra function calls may be slower than just a simple conditional.