Does the lender have to have the appraisal before locking?

No they don't. However, every company has their own policy as to when they allow a loan to be locked. Some will allow locking at the time of application or after the loan is approved.

It depends on the lender. They do not have to by law, but some lenders may have the policy to only lock after an appraisal is completed.

A lender is more apt to require this on a refinance since there typically isn't any way to know what the value is. On a purchase transaction the Realtor has very good idea about the value due their access to recent sales. If a lender locks a loan, this means they are committing to selling that loan on those terms to Fannie Mae, etc. On a refinance the value could come in too low and the loan may need to be canceled. This is very costly to the lender and if it happens too often they can be penalized with higher rates.

Everyone is correct that lenders have their own company rules. The one requirement I know is you have to have a property address to lock a loan since the lock is on the address. If you change properties the lock is invalid. Ask your lender, sometimes rules can be bent to accommodate.

It depends on the lender policy.