For the contact layout in HubSpot, can I set the page layout based on a field value?

Yes this is possible! Steps are as follows:

  1. Go to Record customization on settings (in the contact object)
  2. Choose customize on the left sidebar and then edit the default view
  3. He will need to add and create a new section and make this section conditional
  4. The Property = Record Type; Value = default contact, and then he will choose lead status for the dependent property.