Save current time when Game Over, then compare to new current time and get the difference?

Hello everyone! I'm working on this:

I have 5 actual lives of the 5 Max lives capacity (full lives). When I GameOver I store the current DateTime and Add 30 min. to auto-fill 1 life. If I lose again I'll add 30 more min. to fill another life and so.

Is like that popular mobile games system to refill lives like TwoDots or Folt.

The problem is I have troubles with my code, it is no working :/ I'm not getting the difference between the start of the counter and the actual time. This is my code:

public class myClass : MonoBehaviour {

 public int Max_lives = 5;
 public int Actual_lives;
 DateTime time_start;
 DateTime time_now;
 DateTime last_time;;

 void Start () {
     if (!PlayerPrefs.HasKey("Actual_lives_ready"))
     {
         PlayerPrefs.SetInt("Actual_lives_ready", Max_lives);
     }
 }
 void Update ()
 {
     time_now = DateTime.Now;
     if (Actual_lives < Max_lives)
     {
         for (int aument = Actual_lives; aument < Max_lives; aument++)
         {
             time_start.AddMinutes(30);
             TimeSpan diff = tiempo_now.Subtract(time_start);
             if (time_now >= time_start) // Here I want to get the difference between the two times, I think I dont get it yet. if already pass 30 min after time_start then:
             {
                Actual lives = actual lives + 1;
             }
         }
     }
 }

 public void GameOver()
 {
     if (Actual_lives == Max_lives)
     {
         tiempo_inicio = DateTime.Now;
         PlayerPrefs.SetString("Hour_Start", tiempo_inicio.ToString());
     }
     Actual_lives = Actual_lives - 1;
 }

}