If you haven't already, you will need to map the custom lead field to the custom contact field in Salesforce.
In the Setup Area of SFDC, go to the App Setup Section, Customize, Leads, Fields.Then scroll down to the Lead Custom Fields and Relationships section. Click on the map lead fields box. Find your custom field on the left column and choose the field it maps to on the contact object, then save. The sync should then pick up the relationship between the fields.