Demonstration of LiveData.

CountDownTimerLiveData.java

package net.pside.android.example.sunaba.livedata;

import android.arch.lifecycle.LiveData;
import android.os.CountDownTimer;
import android.util.Log;

import java.util.concurrent.atomic.AtomicBoolean;

public class CountDownTimerLiveData extends LiveData<Long> {

    private static final String TAG = "CountDownTimerLiveData";

    private static CountDownTimerLiveData sInstance;

    public static CountDownTimerLiveData get() {
        if (sInstance == null) {
            sInstance = new CountDownTimerLiveData();
        }
        return sInstance;
    }

    CountDownTimer timer;
    AtomicBoolean timerIsAwaken = new AtomicBoolean(false);

    private CountDownTimerLiveData() {
        timer = new CountDownTimer(5000, 100) {
            @Override
            public void onTick(long millisUntilFinished) {
                setValue(millisUntilFinished);
            }

            @Override
            public void onFinish() {
                setValue(0L);
                timerIsAwaken.set(false);
            }
        };
    }

    @Override
    protected void onActive() {
        Log.d(TAG, "onActive");
        super.onActive();
        if (!timerIsAwaken.get()) {
            timer.start();
            timerIsAwaken.set(true);
        }
    }

    @Override
    protected void onInactive() {
        Log.d(TAG, "onInactive");
        super.onInactive();
//        timer.cancel();
    }
}

MyLifecycleActivity.java

package net.pside.android.example.sunaba;

import net.pside.android.example.sunaba.databinding.ActivityMyLifecycleBinding;
import net.pside.android.example.sunaba.livedata.CountDownTimerLiveData;

import android.arch.lifecycle.LifecycleActivity;
import android.content.Context;
import android.content.Intent;
import android.databinding.DataBindingUtil;
import android.os.Bundle;

public class MyLifecycleActivity extends LifecycleActivity {

    public static Intent createIntent(Context context) {
        Intent intent = new Intent(context, MyLifecycleActivity.class);
        return intent;
    }

    ActivityMyLifecycleBinding binding;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        binding = DataBindingUtil.setContentView(this, R.layout.activity_my_lifecycle);

        CountDownTimerLiveData.get().observe(this, value -> {
            binding.textView.setText(String.valueOf(value));
        });
    }
}

画面回転してもタイマーがリセットされないやつ

You don't need an AtomicBoolean since onActive() and the CountDownTimer callbacks will be called on the main thread.