Editing the record on lightning experience easy with the force:recordEdit component which represents the record edit UI for the specified recordId. force:recordEditcomponent displays fields in the order they appear on the corresponding page layout and record details page. Below is the simple way to use the force:recordEdit which display the edit page and saves button will save the data.
handleSaveSuccess handler will be invoked after the record is saved and shows the toast notification to the user
var toastEvent = $A.get("e.force:showToast");
"message": "The record has been updated successfully."
Create a quick action as shown below and add this action to page layout.
After you click the Edit Contact you can see the model open in edit mode