Bear in mind that if you use/hire a big lens, you will need to shoot with a wide aperture and high ISO. Normally the moon is so bright that even with a 400mm or 600mm lens, you don't need to worry too much about the Earth's rotation, because the shutter speed will be short enough to freeze the motion. However, the moon becomes a lot dimmer during a lunar eclipse, so you will need to be very careful to keep shutter speeds short and not get motion blur at long focal lengths. For example, my shot above was taken at f/8, ISO 800, and required a 2 second exposure, which was too long to avoid picking up the movement of the moon, even at just 250mm.
There's a useful calculator on this page for working out the shutter speed you can use without needing equipment to track the Earth's rotation:
http://www.openphotographicsociety.org/shop-and-tools/calculators-and-utilities/sun-and-moon-calculators/lunar-eclipse-shutter-speed-calculator
(Under the 'miscellaneous camera information' section)
For example, put in a 600mm lens on a 24 megapixel full-frame camera, and you'll see that you need a shutter speed of 1/4 of a second or faster to avoid blur.