Salesforce has an out-of-the box setting to allow skipping validation rules when you CONVERT a Lead.

However, this setting is not available by default if your organization was created sometime before 2010 i believe. You could however, raise a case with Salesforce and they will enable the feature for your i both your production and sandbox instances.

Below is a screenshot of how it looks, if you do not see this option please contact Salesforce customer support and get it enabled.