Sorry for the delay in replying but have been considering this.
To be honest, I have no experience in car leasing here in Portugal.
I do know that car hire companies having been having one devil of a time getting lease financing for their fleets over the past 2 years owing to the economic crisis.
If you are a member of the RAC or AA you might be able to get advice from the Portuguese equivalent, the ACP.
They have an office in Faro just around the corner from the Station.
R. Francisco Barreto 26
8000 Faro
Tel: 289 898 950
Fax: 289802132
email: acpfaro@acp.pt
Hope this helps.