The "IT DEPENDS" is the real answer here......
Lease co can offer lots of things subject to it being in the contract and the customer paying for it. But also they may insist on it because for example the airline does not have airline accredited maintenance facilities that meet the standards required. Think of it as the £200,000 New Merc been serviced by Bob the mechanic in the back street.
This would also apply in terms of an ACMI where the recruiting and training policies are carried out by Brenda whose previous customer experience was a till trainer at Poundland.
This is why no single aircraft lease deal is the same, some airlines pay a significant premium because they have a crap credit rating, some airlines will not be let have an aircraft only lease because nobody trusts their maintenance and crewing or the airline operates in a part of the world where pot shots get taken or parts may go missing.
Whether it is a Financial Lease or Operating Lease will depend on credit rating / capability of airline but also whether fairly specific financial criteria are met. This is why Accountants / Lawyers for Lease co's are very well paid as paperwork gets drawn up in a specific way depending on airline to transfer risk or not as the case may be.
There is no "one size fits all" and even when something appears to be a Finance lease, the reality is it may not be and vice versa.