During a session of free swimming into italian public pool is good practice to occupy always the right side of the lane.
I do not know if it is related to the way of driving car.
In Country like UK, Australia and Japan, where you drive at the left, is there a common behaviour? Which side you tend to swim if you have to share the lane with other athletes?
Correct, most UK pools have lane markers for public sessions which indicate which lanes are clockwise and which are anti-clockwise. These typically alternate but I believe it's less due to the splash (as suggested by Philip Kendall) and more so that swimmers don't clash arms across the lane ropes.
If there are no direction markers then I would just follow what other swimmers are doing in the same lane, or if the lane is empty then look at the adjacent lanes and see whether clockwise or anti-clockwise is more desirable.
Every time I've seen lanes used in the UK, they have always alternated between "swim clockwise" and "swim anticlockwise". This has the advantage that swimmers in alternate lanes are swimming in the same direction, which reduces the amount of splashing.
I was a competitive swimmer for 7 years, and people generally swam counter-clockwise, although there have been rare cases where it is the opposite, at my pool which is the same as how we drive in Canada. There is no strict rule here to which side of the lane you swim on.
However, in warm-up at swimming competitions, the lanes would alternate for two more specific reasons than what Will Appleby said. For one, it helps specifically with avoiding the clashing arms in the stroke butterfly. Secondly, it does help a bit with other strokes in that if you are not right beside someone and the lanes stay in sync, there will be no clashing between lanes, but if someone ends up beside you, it is possible more clashing would result.
