Can I add a custom field that's associated with an opportunity to the lead convert page?

Yes, you can create a custom field for an object and associate it to another object to suit your specific to your business needs. Let's say you want to use an existing custom field that's associated with your opportinity and want to add the custom field so that it's displayed on the lead covert page as part of your leads to opportinity conversion process.

Here are the high-level steps to follow:
  1. Create a custom field in Application Composer for both the Opportunity and Sales Lead objects.
  2. Use the predefined mapping Copy Lead to Opportunity Map to populated the Opportunity custom field with the Lead custom field.