As Tweak says, only laps successfully done in hotlapping mode are valid. I reckon you must have done some laps online, which is why you have seen a record of them at lfs-world (in your online racer stats section). LFS automatically records the number of laps you have done, and your best time at each track in each car, but this is just a personal record of your online laptimes really.
Online laps are not accepted as hotlaps, and so are not shown on the WR charts etc.
In hotlapping mode, just hit "1" after you've done your best time to automatically save the replay with an easily recognisable name.