Multiple threads reading from single List, one thread at the time using Lock.. how?

I currently have the following class:

    public List<DB_ROW> DB = new List<DB_ROW>();
 
     class MY_CLASS
     {
 
         // contructor executes two READER_THREAD's
         public void MY_CLASS()
         {
             Thread reader_thread_1 = new Thread(READER_THREAD);
             Thread reader_thread_2 = new Thread(READER_THREAD);
 
             reader_thread_1.Start();
             reader_thread_2.Start();
         }
 
         // reader thread fetches a single field from the 'global' database
         public void READER_THREAD()
         {
             List<DB_ROW> ORDERED_DB = GLOBAL.DB.OrderByDescending();
             string ID = ORDERED_DB[0].ID;
             GLOBAL.DB[original_index].LAST_USED = NOW(); // update LAST_USED time
         }
     }
 

*The problem is.. * that both threads execute at the same time, therefor they fetch the same 'ID'. I looked into Lock's and modified my class like this:

   public List<DB_ROW> DB = new List<DB_ROW>();
 
     class MY_CLASS
     {
 
         // contructor executes two READER_THREAD's
         public void MY_CLASS()
         {
             Thread reader_thread_1 = new Thread(READER_THREAD);
             Thread reader_thread_2 = new Thread(READER_THREAD);
 
             reader_thread_1.Start();
             reader_thread_2.Start();
         }
 
         static readonly object _locker = (object)GLOBAL.DB;
 
         // reader thread fetches a single field from the 'global' database
         public void READER_THREAD()
         {
             lock(_locker){
                 List<DB_ROW> ORDERED_DB = GLOBAL.DB.OrderByDescending();
                 string ID = ORDERED_DB[0].ID;
                 GLOBAL.DB[original_index].LAST_USED = NOW(); // update LAST_USED time
             }
         }
     }
 

But it doesn't change anything.. The DB List is outside the class, how can I 'lock' it, so only one READER_THREAD reads and updates it at a time?

Also, I have different threads outside this class updating DB as well, will the lock block them from updating the DB too while READER_THREAD is running or will the lock only apply to READER_THREAD (that's what I need)? Thanks!

RESULT I GET NOW:

  READER_THREAD_1: Fetches ID: 1
   READER_THREAD_2: Fetches ID: 1
 

RESULT I WANT:

  READER_THREAD_1: Fetches ID: 1
   READER_THREAD_2: Fetches ID: 2
 

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