I Am A 56 Year Old Woman 5'3 ,135. I

I am a 56 year old woman 5'3 ,135. I workout every morning half hour lifting weights and an hour (3.5 miles)walking on the tread mill. I notice after lifting weights when I go up stairs to the treadmill I get very lightheaded. It lasts one to two minutes and it has been happening more and more frequently. Any suggestions, I don't eat before working out. I'm thinking low blood sugar?