Cut stems off strawberries. Use sharp knife to cut "X" in bottom of each berry, being careful to not cut all the way through strawberry; gently pull pieces apart to create opening in center.

Whisk cream cheese and 1/4 cup milk in medium bowl until blended. Gradually stir in remaining milk. Add dry pudding mix; beat 2 min. Stir in COOL WHIP and lemon zest. Spoon into resealable plastic bag.

Cut small corner from one bottom corner of bag; use to pipe cream cheese mixture into strawberries. Drizzle with chocolate.