The Campaign lookup field on the lead page 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 to associate an existing campaign while on the lead edit screen. Upon this new lead creation if a campaign is associated from this lookup field, when the lead is saved it will add it to the campaign history related list.
This provides the user a shortcut so they don't have to create the new lead filling out the fields on the edit screen, save the lead, then go down to the Campaign History related list section and add the campaign. This reduces the amount of clicks for the user for the initial lead creation. For this reason, when a lead is saved, the campaign lookup field disappears because after the initial lead creation the user is expected to add campaigns through the Campaign History related list.
Regarding mapping the campaign to the Opportunity: When a Lead is converted, the most recently associated campaign is brought over to the Opportunity Campaign Source field upon conversion.
For example, I create a new lead and in the new lead edit screen associate it to "Seminar", save the lead and then later add the "Trade Show" campaign to the lead from the Campaign History related list. When I convert the lead, the Campaign Source on the opportunity will have "Trade Show" in the field because it was the most recent campaign added to the lead. It is assumed that the most recent campaign helped close the deal when tracking the marketing dollars on the campaign, if this is not the case, the Campaign Source on the Opportunity would need to be manually updated.