Please keep in mind that the FAR is not a catch-all and may not always cover every specific situation that arises. Based on the information you’ve presented in this AAP question, I feel it is probably safer to refer you to some additional resources that may help to answer your question. However, the cognizant contracting officer will have the ultimate say over how this is handled by your office, considering all of the pertinent facts and governing documents, including the JTR and the lease terms you already mentioned.

1. FAR subpart 51.2 covers Contractor Use of Interagency Fleet Management System (IFMS) Vehicles – the regulations described therein may or may not pertain to your situation. However there is mention in FAR 51.204 that alludes to authorizing contractors to use IFMS vehicle while complying with the requirements of 41 CFR 101-39 and 41 CFR 101-38.301-1
2. As mentioned immediately above, consult:
   1. 41 CFR 101-39
   2. 41 CFR 101-38.301-1
3.  FedFleet2020__Best_Practices_in_Federal_Fleet_Management_Contractor_Use.pdf (gsa.gov)– In researching this question, I came across this document that looks to be a GSA sponsored presentation. It is relatively recent and contains a number of links and references within.

 Again, please make sure you consult your program’s attorney, the cognizant contracting officer, and all relevant references and resources as you proceed.