There are actually three subspecies of lynx which is not specified in the question. So if I am going to answer the question fully I have to refer to each subspecies of lynx.
The main prey of Canada lynx is the snowshoe hare and they are basically nocturnal although this cat may be found moving about at any time of day. They travel at about 0.75 to 1.46 km/h. They may sit and wait for long periods. The snow on which they are sitting may melt and form an ice-encrusted impression of their body. They may cover between 8 to 9 km a day in their normal activities. If hare densities increase they may travel further.
When independent (adult) and when dispersing from their mother’s home range (natal range) they may travel as much as 500 km in the Yukon Territory, for example. Two Canada lynx were recorded as travelling more than 1,000 km when dispersing to their own home range. Dispersal distances averaged 163 km and range from 17 to 930 km in one study. The sex or age of the individual did not change the distances.
As for Canada lynx, the Eurasian lynx may be lucky to find a home range near their natal range or they may have to travel hundreds of kilometres. In one study they found that lynx travelled between 25 to 92 km when dispersing from their natal range.
As for day-to-day travel, I don’t have specific distances from the reference work that I am using (Wild Cats of the World) but I would expect the distances to be similar to those of Canada lynx.
They travel extensively and visit most parts of their ranges on a regular basis. The average size of a home range is about 10.3 km² for males and 8.7 km² for resident females. In one study an adult male travelled an average of 9.3 km per day over a four-day period. He travelled mostly at night and the distance varied from between 5.9 to 13.6 km. The average distance travelled per day for males was 8.7 km compared with 6.4 km for females in another study.
If you are particularly keen in knowing the exact references for the information provided on this page then please leave a comment and I will respond promptly with the information that you want. In the meantime, please note that the source information is the excellent book Wild Cats of the World authored by Mel Sunquist and Fiona Sunquist, ISBN: 0-226-77999-8. Buy it on Amazon if you want the best information on the wild cats.