Typically after the application fee the lender orders the appraisal. However, unlike pre teh 2008 collapse of the financil market, the lender does not order the appraisal from the appraiser. Rather from an 3rd party who then assigns the appraisal. This last step is completely out of the control of the lender as is the selection of the appraiser. Long story, 1 to 2 weeks.