Do you need to “map” a Lead Custom Field to a Standard Contact Field during conversion?

Not possible! in Salesforce, by concept you can only map Standard Fields to Standard Fields and Custom Fields to Custom Fields but what’s your way around? If you run into this requirement this is how you could do it.

Create a Process that Updates a Field when Converting a Lead into a Contact in Process Builder. Something like this:

Object*: Lead
Start the process*: when a record is created or edited

Node: Name you Node
Criteria for Executing Actions*: Conditions are met
Set Conditions: [Lead]. IsConverted Equals Boolean True
Conditions: All of the conditions are met (AND)

Immediate Actions
Action Name: Name your Action
Record*: [Lead].Converted Contact ID
Criteria for Updating Records*: No criteria—just update the records!

Set new field values for the records you update
Mobile Phone Field Reference [Lead].Home_Phone__cc

Very straightforward. The only tricky part is knowing which field value to update when setting new field values for the records you update. Process Builder shows the Field Labels and not the API field names which can be a little confusing but I recommend checking the SOAP API Developer Guide for those purposes.