Lucky Dags is a Single Target enemy, which makes it very easy when on its own. However, it compensates for this with very high damage and a rapid attack rate, meaning that any cat that gets hit is a lost cause. It is particularly dangerous when stacked, as many Lucky Dagses can attack faster than one can spam cats.
Make sure to spam meatshields at all times. You can prioritize the cheaper ones because Lucky Dags can instantly kill most meatshields other than high leveled Eraser Cat or Manic Eraser Cat. Using high DPS units like Pizza Cat or Assassin BearCat is a good idea, because Lucky Dags can't hit them even if they are in its range. Fast units such as Valkyrie Cat may not work when there are multiple of them, because immediately after the first group of meatshields die, Valkyrie Cat charges ahead of the second group, getting killed instantly.