1. User triggering the process should have the correct record type settings.

2. Error ‘Record Type Unavailable’ when a Lead is converted
https://help.salesforce.com/articleView?id=000329123&type=1&mode=1

Issue during Lead Conversion:
1. Make sure the owner of the record has the correct record type settings.
Database.convertLead():
If the organization uses record types, the default record type of the new owner is assigned to records created during lead conversion.
Reference Articles:
https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_calls_convertlead.htm
https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/langCon_apex_dml_examples_convertlead.htm