For customer input question type data to show inside Klaviyo, it's not enough to define the Variable ID inside Lantern ( that's only for internal analytics purposes). The variable ID must correctly be defined inside the Integration options so that Klaviyo and Mailchimp recognize the value entered - in this example, the customer’s first name.
For Klaviyo , the property for first names already exists inside their system and for it to be recognized when data is sent over, the variable name must be first_name. Same for the variable last_name .
Names are just an example of customer input questions. You may want to ask people about their eye color and create the variable eye_color inside Lantern. For the data to be passed to Klaviyo, it's important that you create a variable for eye color inside Klaviyo as well.
You could give this the same name eye_color inside Klaviyo. After creating it you must come back inside PPF and add eye_color as the Klaviyo ID under the Integration options so that Klaviyo then knows when it receives this information where to send it and what it means.
This article will help you better understand how to create and set up a new variable inside Klaviyo.