So, four months after the alleged contravention, you get a PCN in the post for it and your car is leased.
As this is a lease car, the first PCN would have been sent to the lease company, who can submit representations that they are a lease company and give your name and address as the party leasing the car on the date of the alleged contravention. The council can then cancel the first PCN and issue a second one to the supplied name and address. However, there is a 28 day limit on serving PCNs from date of contravention in the Act under which they have issued the PCN. They have another 28 days to issue the 2nd PCN after cancelling the first, but on he face of it, here it does look as if they are trying it on, and are out-of-time.
However, there is nothing in the Act that imposes a time limit on them receiving reps from the lease company, and then accepting those reps and advising of cancellation. The date of them advising the lease company that they accept their representations is therefore key to the matter. So, you need to request the lease company to supply you with the date of the letter advising them that their reps have been accepted. Count 28 days from that, and if your PCN is dated beyond it, they are out-of-time to issue the PCN.
Of course none of the above even starts to look at whether the contravention occurred at all, so more information is needed if you can remember it. There will be a video, and that is the sole evidence of the alleged contravention. You can probably view this on the Haringey website.
The other aspect is whether your agreement with the lease company is a valid one for the purposes of the Act which refers to "Hire" company. See Schedule 1 Para 1 (9): -
(9)In this paragraph, “vehicle hiring agreement” and “vehicle-hire firm” have the same meanings as in section 66 of the Road Traffic Offenders Act 1988 (c. 53) (Hired vehicles).
The Act they have issued the PCN under is the London Local Authorities & Transport for London Act 2003
https://www.legislation.gov.uk/ukla/2003/3/contents/enacted.
Others on here are far more experienced in the LLA & TfL Act 2003, so wait a bit for more input, but don't miss any deadlines on the PCN.
