To be honest, I haven't read Keyseight, Lecroy or R&S warranties conditions.
I read Tektronix warranties only because I sold an old TDS last year and wanted to know if the next buyer would be protected.
http://www.tek.com/service/warranties/warranty-18
On paper, NO.
Maybe it is different in real life ?
No, if the warranty conditions limit warranty to the original purchaser then that is the case. However, older instruments will be treated in accordance with the warranty conditions that were current when the thing was sold, which may have been different.
But as I said, this is less of a problem with Keysight, LeCroy or R&S as they generally don't do such shenanigans.
Maybe I will consider buying a used oscilloscope in the future but I need an oscilloscope quickly on which I can count.
I will not wait 3 months before finding a rarity on Ebay
There's no need to wait 3 months, for Agilent/Keysight just ask for the S/N and then go to the Keysight website where you can check the warranty status. For LeCroy, contact their support and they'll tell you what warranty is on a scope.
Also, both manufacturers allow you to buy fresh warranty for a scope you bought 2nd hand, provided it is fully functional and still within the mainstream support period. Even when the original warranty has long expired. Keysight calls them "repair agreements", LeCroy just calls it "warranty". And the costs, especially for Keysight gear, can be surprisingly low, and often a younger 2nd hand unit plus repair agreement can give you the same as a brand new unit at a much lower price.
If you are worried about warranty: GW Instek offers a limited lifetime manufacturer warranty on their equipment for the original owner. The warranty ends 5 years after they stop producing the model.
Really? That's a very generous warranty offer, and it shows that they clearly have some confidence in their products.