Hmmm... as system admin, what will you check?
- Make sure Campaign field is added in Lead page layout - checked
- Check Field-Level Security for particluar user profile - checked
User still do not see Campaign field in Lead after it saved or when user edit a Lead, but it is visible when user create new Lead. After some finding, it is designed by default from Salesforce.
Here is the explanation:
1. The Campaign lookup field on the lead page only available when user create new Lead.
2. It will disappears after a new lead is created, because the purpose of this field is to make it easier for the user when creating a new lead and to associate it to an existing campaign.
3. If a campaign is associated from this lookup field on Lead creation process, it will be shown in Campaign History related list. User can add more campaigns from Campaign History related list in Lead Page layout.
If we look to the data structure, Lead Id is a field in CampaignMember object, Setup | Customize | Campaigns | Campaign Members | Fields
When a Lead is converted, the most recently associated campaign is brought over to the Opportunity Campaign Source field upon conversion.
Reference: Why does the Campaign lookup field on the lead page disappear after a new lead is created?