To create a custom email template for the Local Delivery out for delivery event, you can use the following code:
{% if order.shipping_method.carrier_code == 'local_delivery' %}
{% if order.status == 'ready_for_pickup' %}
{% include 'email/local_delivery_out_for_delivery.liquid' %}
{% endif %}
{% endif %}
This code will check if the order’s shipping method is Local Delivery and if the order’s status is Ready for Pickup. If both of these conditions are met, the email/local_delivery_out_for_delivery.liquid template will be included in the email.
You can create a custom email template for the Local Delivery delivered event in the same way. The only difference is that you will need to use the email/local_delivery_delivered.liquid template instead of the email/local_delivery_out_for_delivery.liquid template.
The Help Center page Elias shared has more information on how to edit your notification templates. You can access them from within your admin under Settings > Notifications. If you aren’t comfortable making these kind of changes yourself we recommend hiring a developer to assist you further: Shopify Partner Directory.