We are doing this using a clone of the 'Inbound New Guest Appointment' flow. Keep in mind this is a guest user thru the experience cloud guest user. The other inbound flows 'Inbound New Appointment',..... require the customer to authenticate. We are passing parameters into the flow from the users email card to help with processing. The appointments create a Service Appointment which need to be connected to a Lead, Account, Opportunity,... for the lookup field requirement to be met. Here is a good (long) webinar that the Minnesota user group provided on setting up Lightning Scheduler using the Lightning Scheduler Assistant and a good guide on the data model (which takes some getting use to.)
Some links:
Minnesota Lighting Scheduler Assistant and data model webinar:
https://www.youtube.com/watch?v=KKfoTqLJsYk
Lightning Scheduler Assistant overview:
https://www.youtube.com/watch?v=GkqTXEqfXKk