Leasing new and used aircraft are quite different, especially if used are close to end of life.
For used aircraft, nearly everything is negotiable.
For a new aircraft lease, all leasing companies use their own generic templates, which are not so different between competing companies. Customers will try to negotiate some favourable amendments. The exception are leases to large operators, like the US3, ME3 and EU3, sometimes referred to as Tier one airlines. Tier one airlines have their own generic lease documents, which the leasing companies will seek to fine tune.
The main lease document, which depending how the lease is financed, may or may not be published, includes multiple side agreements (which are never published), covering a multitude of subjects, including end of lease (EOL) condition and payments.
Aircraft and engines are physically inspected by the leasing company's own or contracted staff at regular intervals throughout the lease, and documentation too, and even more thoroughly before return.
Most leases exclude the use of parts pre-dating the build date of the aircraft. So if returning a 12 year old 777, it cannot be returned with documented parts older than 12 years. As preparation for return, the leasor will either require compensation for older parts, or for the parts to be updated.
One side agreement covers utilisation, expressed as hours and cycles for the aircraft, and hours, cycles and 'other' for engines. If for example, the aircraft is returned with more hours than agreed, then the leasee will incur a financial penalty.
There is no saving to the leasee returning an aircraft just hours from major inspections or maintenance, as the pro rata cost of these are documented, and included in the EOL payment. For example, return the aircraft just hours from a major inspection, and the leasee will be up for 99.99% of the cost of the inspection.
Airlines with major maintenance and inspection capability inhouse, will actually operate the aircraft to the limit, and undertake required work inhouse before returning to the leasor, as it provides an opportunity to save EOL costs.
Another side agreement covers the external condition of the aircraft. Mostly they have to be returned white. Again, in some cases, if the airline has inhouse capability, they will do it themselves. Most airlines arrange painting before return, as they do not like the publicity of their aircraft being recognisable in storage, or in use by third parties.
Interiors usually have to be returned in as new condition, but it's common practice to agree a dollar figure, and pay that instead of undertaking the work. Most airlines will attempt to remove all interior branding. This payment gives the leasor some wriggle room to negotiate with new customers.
Just as for a new aircraft, where there is a customer acceptance flight, the same happens on behalf of the leasor before the aircraft is formally returned.
Engine ownership is no longer straightforward. We have airlines buying and leasing (in some cases from the engine OEM's or other leasing companies) engines for the same fleet. We have loan engines from other airlines and the OEM's.
The appetite to participate in commercial aviation finance, means those leasing engines may package 4-6 at a time, and offer them to the market. Those deals may include restrictions, like remaining with the original operator.
Engines purchased in different tranches, may incur different PBTH fees. Or some may be on fixed and others on variable terms. Or if very different ages, with hours and cycles miles apart, and are on variable PBTH contracts, the fees for one could be radically different to another.
So an engine swap, may be to harmonise ownership, and/or PBTH charges.
Engine swaps in the 60's and early 70's, were to return the oldest or worst engines. Those days are long gone.