How to hide search option from lead List view in lightning
As per SalesForce documentation, There is no way to hide the search option.
Only thing, If the user do not have Read on the records in the list permission,he can not Search for records in a list view using the list view search bar.
If You want to hide the List view search bar option, Only thing i can suggest is create an app page using Lightning App Builder and there select a List view of Lead Object and Select hide the List view search bar option.
Use this as a tab by adding it Lightning and mobile application while activating this for users.