Sure! Here's the updated Kotlin code with a new button that adds more elements to the intList and updates the adapter to display the changes:

```kotlin
import android.os.Bundle
import android.view.View
import android.widget.ArrayAdapter
import android.widget.Button
import android.widget.ListView
import androidx.appcompat.app.AppCompatActivity

class MainActivity : AppCompatActivity() {
// Declare variables
private lateinit var listView: ListView
private lateinit var addButton: Button
private lateinit var addIntButton: Button

private val intList = ArrayList<Int>()
private val stringList = ArrayList<String>()

override fun onCreate(savedInstanceState: Bundle?) {
    super.onCreate(savedInstanceState)
    setContentView(R.layout.activity_main)

    // Find UI elements
    listView = findViewById(R.id.list_view)
    addButton = findViewById(R.id.add_button)
    addIntButton = findViewById(R.id.add_int_button)

    // Set up ListView adapter
    val adapter = ArrayAdapter<String>(this, android.R.layout.simple_list_item_1, stringList)
    listView.adapter = adapter

    // Add items to ArrayList when button is clicked
    addButton.setOnClickListener {
        intList.add(1)
        stringList.add("Item ${intList.size}")
        adapter.notifyDataSetChanged()
    }

    // Add more integers to the intList and notify the adapter
    addIntButton.setOnClickListener {
        intList.add(intList.size + 1)
        adapter.notifyDataSetChanged()
    }
}
}
```

In this updated code, we added a new button called addIntButton and initialized it in the onCreate method. When the addIntButton is clicked, we add a new integer to the intList by incrementing the size of the list and then update the adapter to display the new list.

In the activity_main.xml layout file, we can add the following Button element to create the new button:

```xml
<Button
 android:id="@+id/add_int_button"
 android:layout_width="wrap_content"
 android:layout_height="wrap_content"
 android:layout_gravity="center_horizontal"
 android:layout_marginTop="16dp"
 android:text="Add Integer"
 />
```

This will create a new button below the add_button that adds integers to the intList.
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