Yes, the Port Authority of New York and New Jersey owns the M-1 cars and leases them to the LIRR.
The majority of M-3 cars were purchased with funds from the Transportation Bond Act and are owned by the LIRR. I believe several are owned by the PA.
The GP38's were owned by the MTA.
There are differing reasons for doing all this including access to funding, interest rates and availability of funds. BAck in 1968, for example, investors would have been hard to find for a rail system that had few assets and a huge deficit. This would translate into high bonding costs. I believe the PA was able to secure bonds at a better rate because of their cash flow history.
The bonds offered by the MTA at the time were secured by passenger ticket sales. In fact, up until a few years ago, all ticket office bank deposits were placed in a special custodial account to secure bonds. Ticket clerks would remember the funny endorsement stamp they had to put on the checks.
Clem