Hi Matthew,
We spoke on the phone. We'll use LinkedInConnection as our example field.
First thing you want to do is add the field to your Entity table. Next, you can link your LinkedInConnection field to the Contacts table. To do so, click Edit Fields... on your Contacts table and choose Add a Linked Field (see my screenshot below). Now that we have the fields and tables set up, the next phase of your customization project should be to edit the appropriate screens. You'll probably need to add the new field to the New Lead screen, and the new linked field into the Edit Contact screen. Now, when you enter and save data in your new lead screen, it should automatically link to the main contact of the lead.
Let me know if you need anymore help with this.
Jason