Actually, it is true of lithium as well as lead acid, ni-cad or nickel metal hydride.
How many people buy a laptop computer and only rarely take it off mains power? After a year or so, the batteries are useless with only a few minutes life rather than a few hours. The answer is simple - unplug the computer at least once a week and run it on batteries until the batteries are running low. The result will be a laptop battery that will last for 5-10 years rather than giving up the ghost after 1-2 years.
It's true of every electric car I've ever driven as well (and believe me, I've driven a few) and bears up with the tests I've carried out with my Mitsubishi iMiEV. If I charge it up every night having done 10-20 miles, the computed range of the car starts to deteriorate over a period of 10 days or so until it is reporting a total range of around 60 miles. If I drive it so that I'm using most of the range once every week or ten days, the range stays up to over 80 miles. When I drove the car from Coventry to Oxford and back (120 miles with a quick top-up charge in Oxford) the car subsequently reported a range of over 90 miles the following day.
In a real world scenario, making sure that you occasionally end up using most of the charge normally isn't a problem. People's driving pattern change over the period of a week, so if you're only driving 5-10 miles a day during the week, the chances are you'll be driving a lot further at weekends, or visa versa. The chances are you'll be using much more of your range at some point during your usual weekly driving.
The alternative is also valid: if you only ever need to drive 5-10 miles a day, you can quite happily recharge your car every night and top up the batteries. Your range will deteriorate, but then if you're never going that far that won't be a problem anyway.