Example Lock by Code

Obj1.trigger

trigger Obj1 on Obj1 (after insert, after update) {
  Obj1Trigger.handle(Trigger.new);
}

Obj1Trigger.cls

public class Obj1Trigger {
  public static Boolean enforceLock = true;
  
  public static void handle(Obj1[] records) {
    if(enforceLock) {
      Map<Id, Obj11> parents = new Map<Id, Obj11>(
        [SELECT Lock__c FROM Obj11 WHERE Id IN (SELECT Obj11__c FROM Obj1 WHERE Id IN :records)
      );
      for(Obj1 record: records) {
        if(parents.get(record.Obj11__c).Lock__c) {
          record.addError('You cannot edit this record while the parent is locked.');
        }
    }
  }
}

SomeBatchableUpdate.cls

global class SomeBatchableUpdate implements Database.Batchable<Obj1> {
  global Database.QueryLocator start(Database.BatchableContext context) {
    return Database.getQueryLocator([SELECT ... FROM Obj1 WHERE ...]);
  }
  global void execute(Database.BatchableContext context, Obj1[] records) {
    Obj1Trigger.enforceLock = false;
    for(Obj1 record: records) {
      // Do stuff
    }
    update records;
  }
  global void finish(Database.BatchableContext context) {
  
  }
}

thanks a lot @brianmfear