An explanation of how your lure points are added, used, and then displayed in your account:
If you get a new lure, the lure points you scored will be shown as a total. After getting 5 points for a new lure, your score for that lure will show 5/2 where 2 is the number of points required to level up. Leveling up will use the required amount of points. So, having 5/2 points and then leveling up, the lure will use the two required points. Therefore, you'll end up with 3/4 points where 4 is the next required number of lure points to level up.