Well, every fabric can have different effects on color... not to mention your time, temperature and pressure can change the color. The first thing I would do is test your transfers to make sure the color settings are fine. You might want to press something that is 100% polyester at 390 degrees F for around 40-45 seconds with light-to-medium pressure. This will give you some clue as to if your colors look good on polyester. If they don't, you could have some color setting issues.
If the colors look good on the polyester, then you might want to increase your time and temperature of what you are pressing the lycra at. Each fabric will have a different heating point and you certainly don't want to melt the fabric. So you are going to have to do some testing with any fabric to determine what works best for you.
There is also the chance that your heat press temperature might be off. So if you can't figure out what is wrong after doing the two above, then you might want to check the temperature of your heat press with the temperature strips.
The other alternative is to call the company that sold you the system and ask them to assist you. Hope you figure it out. Best wishes,
Mark