Any problems with Low HDL's and trying to lose weight?

I have been diabetic for 10 years and on an Insulin pump for 7 years. In the beginning I was pretty active. Lifes demands, along with age and other factors have caused a major decrease in my level of exercise. At my last Doctor’s appointment, my HDL (which is the good cholesterol) is at a 35. This is really low (the cut off for a low is 45-50) and my doctor states that I am at an increased risk for heart disease. Well at 30 years old, I really don’t want to envision a heart attack so I’ve started back on a work out regimen to increase my good cholesterol levels (and taking my Omega 3’s). My concern is, my nutritionist wants me to lose at least 10 pounds which will also increase my HDL, but the weight doesn’t seem to go anywhere. Is it possible to lose the weight with Type 1 diabetes, and if so how? I am really clueless in this area nad I need to know how to effectively lose the weight without bottoming out and overcompensating for the lows.

I am certainly no expert but what I typically do when I plan to work out at night is eat dinner before hand and try and keep it relatively low carb. I want to get some in there but not a ton, and I wont take any insulin (I use a pen). Even if I have 45 to 60 g of carbs, I will be sitting right around 100 when I get done with a 30-45 min workout. So I always burn of the extra carbs. I have heard that folks with the pump need to turn down their rate a little before they start working out and leave it down afterwards for a few hours. The main thing is to closely monitor your sugars before and afterwards to figure out what works best for you. I have found that I will actually keep burning up some carbs an hour or two after working out as well. Hope that helps some