SharePoint List and Outlook Contact list Sync Issue

Not to my knowledge. The sync only pulls the text values across and lookup columns values include that as part of it. You might be able try making the column some other placeholder name and using an addition calculated value column in the lookup list named Company and have it added to the contact list as an addition column from that list or see if you can reference it in a calculated column named company in the contact list referring the lookup column but if I remember off the top of My head it won’t allow it.