If I may add (I know it's a long thread, but I wanted to add this). First of all - losing weight does not automatically mean losing body fat.

It could mean losing body fat, but it also mean losing water from your body and losing muscle mass. You want to avoid these two as much as you can. Body always wants to get rid of muscles first, because muscles burn the most energy. Body is a very economic "device" and a bit stupid, too
My point is - losing lbs must not be your primary goal - don't pay all attention to figures. A better way is to watch your progress in a mirror!!

In order to lose weight and not lose too much muscle mass one should adapt their diet - without going to much into details (as there really is no need for that) - lower the carbs intake and maintain or even increase protein intake, while intake of fat can be the same (but it is a good idea to consume less trans fat and try to maintain 3 : 1 omega3 : omega6 ratio).

The "big secret" in losing weight (body fat) is no big secret at all. The amount of calories you consume every day must be lower than the amount of calories you burn every day. So you can eat 9000 calories every day - if you burn them than no problem (a bit more on this can be read in this article on how many calories should you eat every day).

So without complicating too much: if you're now 159lbs and want to reach 145lbs than you need to burn roughly 57000 calories. 1 hour of cycling (for your weight) is about 281 calories. Do a little math now. Combine cycling with a little lesser calorie intake via food and you're on faster lane to weight loss. But don't over do this. Eating to less can do your body harm.