I am going to discuss the Canada Lynx initially. I also cover the remaining lynx species namely the Eurasian lynx, bobcat and Iberian lynx.

CANADA LYNX normally travel on the ground and at night i.e. they are terrestrial and nocturnal although sometimes they will travel during the daytime. Sometimes they move between distant parts of their range without stopping or deviating but other times they will zigzag, crossing and re-crossing areas, circling and probing in search of prey. Lynx travel when doing this at between 0.75 to 1.46 km/h. At other times they will sit and wait. They may sit for long enough in the snow to form ice-encrusted impressions of their body.
Not uncommonly lynx travel between 8 to 9 km a day in carrying out the above pursuits. Sometimes they will travel further when the densities of their prey declines. The primary prey of the Canada Lynx, as you may know, is the hare.
Judging by snow tracks made by EURASIAN LYNX, they may travel between 7 and 8 km during a single hunt or as much as 20 km in a day. Studies have concluded that Eurasian lynx travel on average about 10 km per day. However, when there are food shortages, Russian reports describe Lynx travelling huge distances through very harsh winter conditions at the end of which they might have travelled hundreds of kilometres from their normal hunting grounds.
I have already written about BOBCATS and how far they travel but I will summarise it here for the sake of completeness. There have been few studies on how far they travel and how fast. Bobcats appeared to move slowly from 0.1 to 0.6 km/h. Normally they travel at 2.2 km/h when moving daily. It has been estimated that the distance travelled by radio-tagged bobcats range from as little as 2.6 km to 18.5 km per day. Sometimes they travel longer distances during the mating season. Estimating distances travelled by observing their snow tracks produced a similar estimate.
I don’t have information regarding how far IBERIAN LYNX travel daily, due to their rarity I suspect, but I hope that you can extrapolate that from the information provided above.
I can provide full and detailed references for the above information but in the interests of being concise, the information comes from the renowned book on the wild cats by Mel and Fiona Sunquist: Wildcats of the World. Please request full references in a comment or email me (see contact details in top nagivation bar).
SOME MORE ON LYNX:

Canada lynx group hunting improves success rates (Infographic)

The enormous paws of the Canada lynx are a good example of evolution (natural selection)

Infographic on lynx feet

Eurasian lynx- comprehensive page

Do Canada lynx attack humans?

Canada lynx hunting success rate

How big is a Canada lynx?
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