You have the ability to delete a a Lead or Customer record, so long as there is no estimate or order attached to their record.  

From your Lead list or Customer list, click on the edit pencil to edit the led or customer profile. You will then see a 'Delete' option on the bottom-left of the edit form. Again, if the customer has any orders, you will not be able to delete their profile.
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If you can't delete the record due to existing estimates or jobs attached to them, consider 'Deactivating' the lead or custoer record. You can even add some extra to their name like, 'Duplicate' or 'Do Not Use'.